Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Hohm, Olaf; Penas, Victor A.; Riccioni, Fabio
2016-06-01
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O( D, D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O( D, D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
NASA Astrophysics Data System (ADS)
Detournay, Stéphane; Hartman, Thomas; Hofman, Diego M.
2012-12-01
We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the two-dimensional conformal group but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near-horizon geometry of any extremal black hole are identical to those of a two-dimensional field theory with chiral scaling. We consider two examples: black holes in warped AdS3 in topologically massive gravity and in string theory. In both cases, the density of states in the two-dimensional field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Holographic effective field theories
NASA Astrophysics Data System (ADS)
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
Supersymmetric Quantum Field Theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2005-03-01
We consider some supersymmetric multiplets in a purely quantum framework. A crucial point is to ensure the positivity of the scalar product in the Hilbert space of the quantum system. For the vector multiplet we obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. Then we consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
NASA Astrophysics Data System (ADS)
Choy, Ting-Pong
One of the leading problems in condensed matter physics is what state of matter obtain when there is a strong Coulomb repulsion between the electrons. One of the exotic examples is the high temperature superconductivity which was discovered in copper-oxide ceramics (cuprates) over twenty years ago. Thus far, a satisfactory theory is absent. In particular, the nature of the electron state outside the superconducting phase remains controversial. In analogy with the BCS theory of a conventional superconductor, in which the metal is well known to be a Fermi liquid, a complete understanding of the normal state of cuprate is necessary prior to the study of the superconducting mechanism in the high temperature superconductors. In this thesis, we will provide a theory for these exotic normal state properties by studying the minimal microscopic model which captures the physics of strong electron correlation. Even in such a simple microscopic model, striking properties including charge localization and presence of a Luttinger surface resemble the normal state properties of cuprate. An exact low energy theory of a doped Mott insulator will be constructed by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular, a charge 2e bosonic field which is not made out of elemental excitations emerges at low energies. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green function vanishes. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. We show that many of the normal state properties of the cuprates can result from this new charge
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2008-08-15
Free scalar field theory on 2-dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using loop quantum gravity (LQG) type 'polymer' representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation-annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the 'triangulation'-dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non-Fock nature of the representation ensures that the group of conformal isometries as well as that of the gauge transformations generated by the constraints are represented in an anomaly free manner. Semiclassical states can be analyzed at the gauge invariant level. It is shown that 'physical weaves' necessarily underlie such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.
Kirby S. Chapman; Sarah R. Nuss-Warren
2007-02-01
The objective of this project is to identify, develop, test, and commercialize emissions control and monitoring technologies that can be implemented by exploration and production (E&P) operators to significantly lower the cost of environmental compliance and expedite project permitting. The project team takes considerable advantage of the emissions control research and development efforts and practices that have been underway in the gas pipeline industry for the last 12 years. These efforts and practices are expected to closely interface with the E&P industry to develop cost-effective options that apply to widely-used field and gathering engines, and which can be readily commercialized. The project is separated into two phases. Phase 1 work establishes an E&P industry liaison group, develops a frequency distribution of installed E&P field engines, and identifies and assesses commercially available and emerging engine emissions control and monitoring technologies. Current and expected E&P engine emissions and monitoring requirements are reviewed, and priority technologies are identified for further development. The identified promising technologies are tested on a laboratory engine to confirm their generic viability. In addition, a full-scale field test of prototype emissions controls will be conducted on at least ten representative field engine models with challenging emissions profiles. Emissions monitoring systems that are integrated with existing controls packages will be developed. Technology transfer/commercialization is expected to be implemented through compressor fleet leasing operators, engine component suppliers, the industry liaison group, and the Petroleum Technology Transfer Council. This topical report discusses work completed during Phase 1 of the project Cost Effective Reciprocating Engine Emissions Control and Monitoring for E&P Field and Gathering Engines. In this report information, data, and results are compiled and summarized from quarterly
Vector field theories in cosmology
Tartaglia, A.; Radicella, N.
2007-10-15
Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so-called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (cosmic defect theory). We show that the latter fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, while other vector theories use much more. The Newtonian limits are also compared. Finally we show that the cosmic defect theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Resolving Witten's superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2014-04-01
We regulate Witten's open superstring field theory by replacing the picturechanging insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A ∞ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
String field theory and tachyon field
NASA Astrophysics Data System (ADS)
Yang, Yi
In this thesis, we study Sen's conjecture on tachyon condensation by using string field theories, i.e. boundary string field theory (BSFT) and cubic string field theory (CSFT). In the BSFT side, the first explicit calculation of effective tachyon action for the bosonic string was given by Witten ten years ago and by many other authors in the last two years. It was extended to the superstring case shortly after. In our work, we give an explicit calculation of Green functions for the fermionic fields and compute the effective tachyon action for the superstring. The results we obtain agree with earlier results. We then generalize the BSFT method to one loop level. The tachyon condensation at one loop level is systematically studied, and many interesting results are obtained which verify Sen's conjecture. We also apply this method to the non-orientable theory at one loop level, where the expected divergence cancellation is reproduced and the similar effective tachyon action is obtained. By using the boundary state formalism, we verify the duality between open and closed strings. In the CSFT side, since there is no known solution to this theory, tachyon condensation can only be studied by numerical methods, i.e. level truncation. However, at the tachyon vacuum, CSFT is simplified to vacuum string field theory (VSFT) which has a solution - sliver state. By adding a tachyon vertex to the boundary of the sliver state, we have calculated the effective action.
Introduction to Statistical Field Theory
NASA Astrophysics Data System (ADS)
Brézin, Edouard
2010-07-01
1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the φ4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Field-theory methods in coagulation theory
Lushnikov, A. A.
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Field-theory methods in coagulation theory
NASA Astrophysics Data System (ADS)
Lushnikov, A. A.
2011-08-01
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W( Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = { n 1, n 2, ..., n g , ...}, where n g is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional Ψ for the probability W( Q, t). The time evolution of Ψ is described by an equation that is similar to the Schrödinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Study of Low Temperature Baking Effect on Field Emission on Nb Samples Treated by BEP, EP, and BCP
Andy Wu, Song Jin, Robert Rimmer, Xiang Yang Lu, K. Zhao, Laura MacIntyre, Robert Ike
2010-05-01
Field emission is still one of the major obstacles facing Nb superconducting radio frequency (SRF) community for allowing Nb SRF cavities to reach routinely accelerating gradient of 35 MV/m that is required for the international linear collider. Nowadays, the well know low temperature backing at 120 oC for 48 hours is a common procedure used in the SRF community to improve the high field Q slope. However, some cavity production data have showed that the low temperature baking may induce field emission for cavities treated by EP. On the other hand, an earlier study of field emission on Nb flat samples treated by BCP showed an opposite conclusion. In this presentation, the preliminary measurements of Nb flat samples treated by BEP, EP, and BCP via our unique home-made scanning field emission microscope before and after the low temperature baking are reported. Some correlations between surface smoothness and the number of the observed field emitters were found. The observed experimental results can be understood, at least partially, by a simple model that involves the change of the thickness of the pent-oxide layer on Nb surfaces.
Exceptional field theory: SL(5)
NASA Astrophysics Data System (ADS)
Musaev, Edvard T.
2016-02-01
In this work the exceptional field theory formulation of supergravity with SL (5) gauge group is considered. This group appears as a U-duality group of D = 7 maximal supergravity. In the formalism presented the hidden global duality group is promoted into a gauge group of a theory in dimensions 7+number of extended directions. This work is a continuation of the series of works for E 8,7,6 , SO (5 , 5) and SL (3) × SL (2) duality groups.
Field theory for string fluids
NASA Astrophysics Data System (ADS)
Schubring, Daniel; Vanchurin, Vitaly
2015-08-01
We develop a field theory description of nondissipative string fluids and construct an explicit mapping between field theory degrees of freedom and hydrodynamic variables. The theory generalizes both a perfect particle fluid and pressureless string fluid to what we call a perfect string fluid. Ideal magnetohydrodynamics is shown to be an example of the perfect string fluid whose equations of motion can be obtained from a particular choice of the Lagrangian. The Lagrangian framework suggests a straightforward extension of the perfect string fluid to more general anisotropic fluids describing higher dimensional branes such as domain walls. Other modifications of the Lagrangian are discussed which may be useful in describing relativistic superfluids and fluids containing additional currents.
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
Rearranging Pionless Effective Field Theory
Martin Savage; Silas Beane
2001-11-19
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
NASA Astrophysics Data System (ADS)
Tzeferacos, Petros; Daley, Christopher; Fatenejad, Milad; Flocke, Norbert; Graziani, Carlo; Lamb, Donald Q.; Lee, Dongwook; Scopatz, Anthony; Weide, Klaus; Doyle, Hugo; Gregori, Gianluca; Meinecke, Jena; Reville, Brian; Miniati, Francesco
2013-10-01
The process of generation and amplification of Biermann battery magnetic fields is closely linked to the development of turbulence. In an astrophysical environment, a small seed field can be formed in asymmetric supernova remnant blast waves due to misaligned pressure and density gradients. Inhomogeneities in the density distribution can cause the flow to become turbulent and the B-field can be amplified via dynamo action. In this context, the COSMOLAB team will perform experiments using the Omega EP laser at LLE, that represent a scaled-down model of the astrophysical process in a controlled environment. The experiments involve the illumination of a slab-like target, which produces a plasma flow and a Biermann battery field. The flow then propagates through a grid that creates turbulence and amplifies the field. In this study we describe 2D and 3D radiative MHD simulations of the experimental setup, carried out using the FLASH code on Mira (BG/Q) at ALCF. The objective of these simulations is to explore the morphology and strength of the B-fields generated by ablation of target material by the laser, and their amplification due to the grid. This work was supported by DOE NNSA ASC.
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Effective field theory in nuclear physics
Martin J. Savage
2000-12-12
I review recent developments in the application of effective field theory to nuclear physics. Emphasis is placed on precision two-body calculations and efforts to formulate the nuclear shell model in terms of an effective field theory.
Effective field theory, past and future
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2016-02-01
I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.
Vertex operator algebras and conformal field theory
Huang, Y.Z. )
1992-04-20
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Non-Perturbative Field Theories.
NASA Astrophysics Data System (ADS)
Stephenson, David
Available from UMI in association with The British Library. Requires signed TDF. Some non-perturbative aspects of field theories are studied by applying lattice gauge theory techniques. The low-lying hadronic mass spectrum is calculated numerically using quenched lattice quantum chromodynamics. The results of large numerical simulations performed on a distributed array processor are presented and analysed. Particular emphasis is stressed upon the understanding of systematic and statistical errors in the calculation. In addition, the pion decay constant and the chiral condensate are evaluated. An attempt is made to relate the numerical findings to the experimentally measured quantities. A pioneering attempt to understand Yukawa couplings is discussed. A toy Fermion-Higgs system is studied numerically on a transputer array. Dynamical fermions are included in the investigation of the behavior of the system over a wide range of Yukawa couplings. A phase diagram is found for the model which shows evidence of spontaneous chiral symmetry breaking transitions. Extensions of the model are discussed together some speculations concerning the behaviour of Yukawa couplings in general. The possibility of using the lattice as a model for space-time is investigated by studying the propagation of particles on a fractal lattice. In addition, the use of truncated fractals as novel regulators is studied numerically in the hope that the problem of fermion doubling will be alleviated.
Group field theory with noncommutative metric variables.
Baratin, Aristide; Oriti, Daniele
2010-11-26
We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action. PMID:21231377
Perturbative double field theory on general backgrounds
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Marques, Diego
2016-01-01
We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as S U (2 )≃S3 with H -flux. In the full string theory this corresponds to a Wess-Zumino-Witten background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler, and Lüst. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Homotopy Classification of Bosonic String Field Theory
NASA Astrophysics Data System (ADS)
Münster, Korbinian; Sachs, Ivo
2014-09-01
We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.
Kirby S. Chapman; Sarah R. Nuss-Warren
2006-12-31
This report highlights work done on a project intended to lower the cost of environmental compliance and expedite project permitting for Exploration and Production (E&P) operators by identifying, developing, testing, and commercializing emissions control and monitoring technologies. Promising technologies have already been identified and developed. Current work focuses on testing these promising technologies. Specifically, several technologies are being tested in the laboratory for application to lean-burn engines or fully characterized on-site for use with rich-burn engines. Upon completion of these tests, the most cost-effective and robust technologies will be tested in the field and commercialization will ensue. During this quarter, progress in laboratory testing for lean-burn engines was limited by maintenance issues on the KSU Ajax DP-115. The difficulties that required maintenance to be performed will likely require that the 180 psig prototype valve be tested in the future, if possible. The maintenance was performed, and it is expected that the Ajax will be available for testing in the coming quarter. Although laboratory testing was slowed as a result of maintenance issues, progress in experimental characterization of technologies has been significant. NSCR systems will be characterized as applied to rich-burn engines on-site. This characterization will ensure high-quality data in final field testing on rich-burn engines and is considered to be essential, despite that the work requires the delay of official field testing until 2008. Many preliminary and administrative tasks have been completed, including initial site selection, official proposal submittal, and beginning a process to approve necessary changes to installed field engines.
Towards weakly constrained double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2016-08-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Singularity theory and N = 2 superconformal field theories
Warner, N.P.
1989-01-01
The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs.
Gauge anomalies in an effective field theory
Preskill, J. )
1991-09-01
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
Logarithmic operators and logarithmic conformal field theories
NASA Astrophysics Data System (ADS)
Gurarie, Victor
2013-12-01
Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c = -2 and c = 0 logarithmic conformal field theories. c = 0 logarithmic conformal field theories are especially interesting since they describe some of the critical points of a variety of longstanding problems involving a two dimensional quantum particle moving in a spatially random potential, as well as critical two dimensional self-avoiding random walks and percolation. Lack of classification of logarithmic conformal field theories remains a major impediment to progress towards finding complete solutions to these problems.
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
Three approaches to classical thermal field theory
NASA Astrophysics Data System (ADS)
Gozzi, E.; Penco, R.
2011-04-01
In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Descent relations in cubic superstring field theory
NASA Astrophysics Data System (ADS)
Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.
2008-01-01
The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations langleV2|V1rangle and langleV3|V1rangle in the NS fermionic string field theory in the κ and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
E11 and exceptional field theory
NASA Astrophysics Data System (ADS)
Tumanov, Alexander G.; West, Peter
2016-04-01
We argue that the exceptional field theory is a truncation of the nonlinear realisation of the semi-direct product of E11 and its first fundamental as proposed in 2003. Evaluating the simple equations of the E11 approach, and using the commutators of the E11 algebra, we find the local variations of the fields of exceptional field theory after making a radical truncation. This procedure does not respect any of the higher level E11 symmetries and so these are lost. We suggest that the need for the section condition in the exceptional field theory could be a consequence of the truncation.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
Keith Hohn; Sarah R. Nuss-Warren
2011-08-31
This final report describes a project intended to identify, develop, test, and commercialize emissions control and monitoring technologies that can be implemented by E&P operators to significantly lower their cost of environmental compliance and expedite project permitting. Technologies were installed and tested in controlled laboratory situations and then installed and tested on field engines based on the recommendations of an industry-based steering committee, analysis of installed horsepower, analysis of available emissions control and monitoring technologies, and review of technology and market gaps. The industry-recognized solution for lean-burn engines, a low-emissions-retrofit including increased airflow and pre-combustion chambers, was found to successfully control engine emissions of oxides of nitrogen (NO{sub X}) and carbon monoxide (CO). However, the standard non-selective catalytic reduction (NSCR) system recognized by the industry was found to be unable to consistently control both NO{sub X} and CO emissions. The standard NSCR system was observed to produce emissions levels that changed dramatically on a day-to-day or even hour-to-hour basis. Because difficulties with this system seemed to be the result of exhaust gas oxygen (EGO) sensors that produced identical output for very different exhaust gas conditions, models were developed to describe the behavior of the EGO sensor and an alternative, the universal exhaust gas oxygen (UEGO) sensor. Meanwhile, an integrated NSCR system using an advanced, signal-conditioned UEGO sensor was tested and found to control both NO{sub X} and CO emissions. In conjunction with this project, advanced monitoring technologies, such as Ion Sense, and improved sensors for emissions control, such as the AFM1000+ have been developed and commercialized.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2010-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Yang, Guang; Ren, Zhen; Mei, Yan-Ai
2015-10-01
Previous work from both our lab and others have indicated that exposure to 50 Hz magnetic fields (ELF-MF) was able to modify ion channel functions. However, very few studies have investigated the effects of MF on γ-aminobutyric acid (GABA) type A receptors (GABA(A) Rs) channel functioning, which are fundamental to overall neuronal excitability. Here, our major goal is to reveal the potential effects of ELF-MF on GABA(A) Rs activity in rat cerebellar granule neurons (CGNs). Our results indicated that exposing CGNs to 1 mT ELF-MF for 60 min. significantly increased GABA(A) R currents without modifying sensitivity to GABA. However, activation of PKA by db-cAMP failed to do so, but led to a slight decrease instead. On the other hand, PKC activation or inhibition by PMA or Bis and Docosahexaenoic acid (DHA) mimicked or eliminated the field-induced-increase of GABA(A) R currents. Western blot analysis indicated that the intracellular levels of phosphorylated PKC (pPKC) were significantly elevated after 60 min. of ELF-MF exposure, which was subsequently blocked by application of DHA or EP1 receptor-specific (prostaglandin E receptor 1) antagonist (SC19220), but not by EP2-EP4 receptor-specific antagonists. SC19220 also significantly inhibited the ELF-MF-induced elevation on GABA(A) R currents. Together, these data obviously demonstrated for the first time that neuronal GABA(A) currents are significantly increased by ELF-MF exposure, and also suggest that these effects are mediated via an EP1 receptor-mediated PKC pathway. Future work will focus on a more comprehensive analysis of the physiological and/or pathological consequences of these effects. PMID:26176998
Yang, Guang; Ren, Zhen; Mei, Yan-Ai
2015-01-01
Previous work from both our lab and others have indicated that exposure to 50 Hz magnetic fields (ELF-MF) was able to modify ion channel functions. However, very few studies have investigated the effects of MF on γ-aminobutyric acid (GABA) type A receptors (GABAARs) channel functioning, which are fundamental to overall neuronal excitability. Here, our major goal is to reveal the potential effects of ELF-MF on GABAARs activity in rat cerebellar granule neurons (CGNs). Our results indicated that exposing CGNs to 1 mT ELF-MF for 60 min. significantly increased GABAAR currents without modifying sensitivity to GABA. However, activation of PKA by db-cAMP failed to do so, but led to a slight decrease instead. On the other hand, PKC activation or inhibition by PMA or Bis and Docosahexaenoic acid (DHA) mimicked or eliminated the field-induced-increase of GABAAR currents. Western blot analysis indicated that the intracellular levels of phosphorylated PKC (pPKC) were significantly elevated after 60 min. of ELF-MF exposure, which was subsequently blocked by application of DHA or EP1 receptor-specific (prostaglandin E receptor 1) antagonist (SC19220), but not by EP2-EP4 receptor-specific antagonists. SC19220 also significantly inhibited the ELF-MF-induced elevation on GABAAR currents. Together, these data obviously demonstrated for the first time that neuronal GABAA currents are significantly increased by ELF-MF exposure, and also suggest that these effects are mediated via an EP1 receptor-mediated PKC pathway. Future work will focus on a more comprehensive analysis of the physiological and/or pathological consequences of these effects. PMID:26176998
Relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Ring, Peter; Zhao, Pengwei
In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.
An introduction to conformal field theory
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.
2000-04-01
A comprehensive introduction to two-dimensional conformal field theory is given. The structure of the meromorphic subtheory is described in detail, and a number of examples are presented explicitly. Standard constructions such as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Zhu's algebra in classifying highest weight representations is elucidated. The fusion product of two representations and the corresponding fusion rules are defined, and Verlinde's formula is explained. Finally, higher correlation functions are considered, and the polynomial relations of Moore and Seiberg and the quantum group structure of chiral conformal field theory are discussed. The treatment is relatively general and also allows for a description of less well known classes of theories such as logarithmic conformal field theories.
A nonlinear field theory of deformable dielectrics
NASA Astrophysics Data System (ADS)
Suo, Zhigang; Zhao, Xuanhe; Greene, William H.
Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.
Quantum statistical correlations in thermal field theories: Boundary effective theory
Bessa, A.; Brandt, F. T.; Carvalho, C. A. A. de; Fraga, E. S.
2010-09-15
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field {phi}{sub c}, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schroedinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field {phi}{sub c}, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Weyl's Abandonment of Unified Field Theory
NASA Astrophysics Data System (ADS)
Sieroka, Norman
2015-01-01
In 1918, Hermann Weyl proposed a generalisation of Riemannian geometry, in order to unify general relativity and electrodynamics. This paper investigates the physical, mathematical and philosophical reasons for his subsequent abandonment of any such attempt towards a unified field theory.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Reductionism, emergence, and effective field theories
NASA Astrophysics Data System (ADS)
Castellani, Elena
In recent years, a "change in attitude" in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
Conserved currents of double field theory
NASA Astrophysics Data System (ADS)
Blair, Chris D. A.
2016-04-01
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.
Effective field theory out of equilibrium: Brownian quantum fields
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-06-01
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Entanglement entropy in warped conformal field theories
NASA Astrophysics Data System (ADS)
Castro, Alejandra; Hofman, Diego M.; Iqbal, Nabil
2016-02-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL (2, ℝ) × U (1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory
NASA Astrophysics Data System (ADS)
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010), 10.1103/PhysRevE.81.061102; J. Stat. Phys. 149, 643 (2012), 10.1007/s10955-012-0610-y; J. Stat. Phys. 152, 159 (2013), 10.1007/s10955-013-0755-3; Phys. Rev. E 83, 041125 (2011), 10.1103/PhysRevE.83.041125] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Effective Field Theories, Reductionism and Scientific Explanation
NASA Astrophysics Data System (ADS)
Hartmann, Stephan
Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation.
Quantum Cylindrical Waves and Parametrized Field Theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space-time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space-time and review the relevant results for unitary implementability.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
Non Perturbative Aspects of Field Theory
Bashir, A.
2009-04-20
For any quantum field theory (QFT), there exists a set of Schwinger-Dyson equations (SDE) for all its Green functions. However, it is not always straight forward to extract quantitatively exact physical information from this set of equations, especially in the non perturbative regime. The situation becomes increasingly complex with growing number of external legs. I give a qualitative account of the hunt for the non perturbative Green functions in gauge theories.
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Kirby S. Chapman; Allen J. Adriani
2004-01-01
For the period of the 8th reporting period high-impact control technologies were identified during the meeting at Cooper in Oklahoma City. The technologies that were identified will be tested on the Ajax DP-115 engine and are capable of being widely utilized by the E&P industry. Two major areas where engine controls and ignition systems, but still included were other alternatives to reduce emissions. The most exhilarating item for this quarter was when Ajax engine was delivered to the test bed at the NGML.
Kirby S. Chapman
2003-12-01
During the second reporting period, the project team focused on identifying promising technologies that can then be used to monitor and control emissions from E&P engines. These technologies include control and monitoring technologies and in most cases can be used to monitor engine performance as well as control and monitor engine emissions. The project team also identified three potential sources to receive a Cooper Ajax engine that is approximately 100 bhp. The goal is to have this engine delivered to the project team by the end of the calendar year 2003. This will then allow the team to prepare the engine for testing at Ricardo in early 2004.
Global anomalies and effective field theory
NASA Astrophysics Data System (ADS)
Golkar, Siavash; Sethi, Savdeep
2016-05-01
We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on thermal effective field theory, where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient (up to an overall additive factor). This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
On the History of Unified Field Theories
NASA Astrophysics Data System (ADS)
Goenner, Hubert F. M.
2004-02-01
This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin - with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger's or Dirac's equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopocraphical remarks are included.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
The Mean-Field Flux Pinning Theory
NASA Astrophysics Data System (ADS)
Stejic, George
We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with the remarkable observation of Cardy that the horizontal crossing probability of critical percolation may be computed analytically within the formalism of boundary conformal field theory. Cardy’s derivation relies on certain implicit assumptions which are shown to lead inexorably to indecomposable modules and logarithmic singularities in correlators. For this, a short introduction to the fusion algorithm of Nahm, Gaberdiel and Kausch is provided. While the percolation logarithmic conformal field theory is still not completely understood, there are several examples for which the formalism familiar from rational conformal field theory, including bulk partition functions, correlation functions, modular transformations, fusion rules and the Verlinde formula, has been successfully generalized. This is illustrated for three examples: the singlet model \\mathfrak {M} (1,2), related to the triplet model \\mathfrak {W} (1,2), symplectic fermions and the fermionic bc ghost system; the fractional level Wess-Zumino-Witten model based on \\widehat{\\mathfrak {sl}} \\left( 2 \\right) at k=-\\frac{1}{2}, related to the bosonic βγ ghost system; and the Wess-Zumino-Witten model for the Lie supergroup \\mathsf {GL} \\left( 1 {\\mid} 1 \\right), related to \\mathsf {SL} \\left( 2 {\\mid} 1 \\right) at k=-\\frac{1}{2} and 1, the Bershadsky-Polyakov algebra W_3^{(2)} and the Feigin-Semikhatov algebras W_n^{(2)}. These examples have been chosen because they represent the most accessible, and most useful, members of the three best-understood families of logarithmic conformal field theories. The logarithmic minimal models \\mathfrak {W} (q,p), the fractional level Wess-Zumino-Witten models, and the Wess-Zumino-Witten models on Lie supergroups (excluding \\mathsf {OSP} \\left( 1 {\\mid} 2n \\right)). In this review, the emphasis lies on the representation theory
Double field theory: a pedagogical review
NASA Astrophysics Data System (ADS)
Aldazabal, Gerardo; Marqués, Diego; Núñez, Carmen
2013-08-01
Double field theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions and present a brief parcours on worldsheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.
Causality constraints in conformal field theory
NASA Astrophysics Data System (ADS)
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Effective Field Theory in Nuclear Astrophysics
NASA Astrophysics Data System (ADS)
Chen, Jiunn-Wei
2001-04-01
I will discuss some basic ideas of effective field theory and its application to two nucleon systems. The theory allows a perturbative treatment of strongly interacting, bound state problems such that the calculations can be systematically improved and reliable error estimation performed. Also, the field theory formalism naturally allows manifest incorporation of symmetry properties such as gauge symmetry and Lorentz symmetry. Emphasis will be placed on some high precision calculations to low energy astrophysical problems: neutron radiative capture onto proton which is relevant to big-bang nucleosynthesis; neutrino deuteron inelastic scattering employed in the solar neutrino detection by Sudbury Neutrino Observatory (SNO) and the proton-proton solar fusion process which is an important process to fuel the sun. The last two classes of processes share the same two-body operator which is proposed to be measured at ORLAND and could serve to calibrate SNO and the solar fusion rate.
Global effects in quaternionic quantum field theory
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.
1996-12-01
We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and nonbaryonic hot dark matter candidates.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
Prequantum Classical Statistical Field Theory: Fundamentals
Khrennikov, Andrei
2011-03-28
We present fundamentals of a prequantum model with hidden variables of the classical field type. In some sense this is the comeback of classical wave mechanics. Our approach also can be considered as incorporation of quantum mechanics into classical signal theory. All quantum averages (including correlations of entangled systems) can be represented as classical signal averages and correlations.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Kirby S. Chapman; Allen J. Adriani
2005-04-01
During the eighth reporting period, high-impact monitoring and control technologies were identified during a series of meetings at Ajax/Cooper in Oklahoma City. Many of the technologies that were identified will be tested on the Ajax DP-115 engine and are capable of being widely utilized by the E&P industry. Two major areas were engine controls and ignition systems but still included other alternatives to reduce emissions. Another major advance was the completion of setting the Ajax DP-115 engine. This includes anchoring and leveling the engine. Shortly after the engine was prepared, all the necessary utilities were installed. Once the utilities were installed the engine was successfully operated over its normal operating range at the end of the reporting period.
Kirby S. Chapman
2004-01-01
During the fourth reporting period, the project team investigated the Non-Selective Catalytic Reduction technologies that are in use on rich-burn four-stroke cycle engines. Several engines were instrumented and data collected to obtain a rich set of engine emissions and performance data. During the data collection, the performance of the catalyst under a variety of operating conditions was measured. This information will be necessary to specify a set of sensors that can then be used to reliably implement NSCRs as plausible technologies to reduce NOx emissions for four-stroke cycle engines used in the E&P industry. A complete summary all the technologies investigated to data is included in the report. For each technology, the summary includes a description of the process, the emission reduction that is to be expected, information on the cost of the technology, development status, practical considerations, compatibility with other air pollutant control technologies, and any references used to obtain the information.
Effective Field Theory for Jet Processes
NASA Astrophysics Data System (ADS)
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-01
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.
Effective Field Theory for Jet Processes.
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-13
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms. PMID:27232017
Quantum stability of chameleon field theories.
Upadhye, Amol; Hu, Wayne; Khoury, Justin
2012-07-27
Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m<0.0073(ρ/10 g cm(-3))(1/3) eV for gravitational-strength coupling whereas fifth force experiments place a lower bound of m>0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073
A computational theory of visual receptive fields.
Lindeberg, Tony
2013-12-01
A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative
Quantization of non-local field theory and string field theory
NASA Astrophysics Data System (ADS)
Hata, Hiroyuki
1989-02-01
The interaction vertex in covariant string field theory (SFT) is non-local in the time coordinate and the conventional canonical quantization is inapplicable to it. As an approach to quantizing this system we apply Hayashi's theory of the Hamilton formalism for field theories with non-local interactions. We find that the resulting one-loop amplitudes in covariant closed SFT coincide with those in the light-cone gauge SFT. I would like to thank T. Kugo, H. Kunitomo, M.M. Nojiri, K. Ogawa and K. Suehiro for valuable discussions, and especially Professor S. Tanaka for directing my attention to Hayashi's theory.
Transformations among large c conformal field theories
NASA Astrophysics Data System (ADS)
Jankiewicz, Marcin; Kephart, Thomas W.
2006-06-01
We show that there is a set of transformations that relates all of the 24 dimensional even self-dual (Niemeier) lattices, and also leads to non-lattice objects some of which can perhaps be interpreted as a basis for the construction of holomorphic conformal field theory. In the second part of this paper, we extend our observations to higher-dimensional conformal field theories build on extremal partition functions, where we generate c=24k theories. We argue that there exists generalizations of the c=24 models based on Niemeier lattices and of the non-Niemeier spin-1 theories. The extremal cases have spectra decomposable into the irreducible representations of the Fischer-Griess Monster. This additional symmetry leads us to conjecture that these extremal theories, as well as the higher-dimensional analogs of the group lattice bases Niemeiers, will eventually yield to a full construction of their associated CFTs. We observe interesting periodicities in the coefficients of extremal partition functions and characters of the extremal vertex operator algebras.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
A Field Theory Problem Relating to Questions in Hyperfield Theory
NASA Astrophysics Data System (ADS)
Massouros, Ch. G.
2011-09-01
M. Krasner introduced the notions of the hypefield and the hyperring in 1956. Much later, he constructed the quotient hyperfield/hyperrring, using a field/ring and a subgroup of its multiplicative group/semigroup. The existence of non-quotient hyperfields and hyperrings was an essential question for the self-sufficiency of the theory of hyperfields and hyperrings vis-à-vis that of fields and rings. The momogene hyperfield, which was introduced by the author, is a hyperfield H having the property x - x = H for all x≠0. The existence of non-quotient monogene hyperfields is a hitherto open question. The answer to this question is directly connected with the answer to the question which fields can be expressed as a difference of a subgroup of their multiplicative group from itself and which these subgroups are. These issues, as well as some relevant theorems are presented in this paper.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Marginal deformations of nonrelativistic field theories
NASA Astrophysics Data System (ADS)
Mallayev, Davron; Vázquez-Poritz, Justin F.; Zhang, Zhibai
2014-11-01
We construct the supergravity duals of marginal deformations of a (0, 2) Landau-Ginsburg theory that describes the supersymmetric lowest Landau level. These deformations preserve supersymmetry and it is proposed that they are associated with the introduction of a phase in the (0, 2) superpotential. We also consider marginal deformations of various field theories that exhibit Schrödinger symmetry and Lifshitz scaling. This includes countably infinite examples with dynamical exponent z =2 based on the Sasaki-Einstein spaces Yp ,q and Lp ,q ,r, as well as an example with general dynamical exponent z ≥1 .
Bayesian parameter estimation for effective field theories
NASA Astrophysics Data System (ADS)
Wesolowski, Sarah; Klco, Natalie; Furnstahl, Richard; Phillips, Daniel; Thapilaya, Arbin
2015-10-01
We present a procedure based on Bayesian statistics for effective field theory (EFT) parameter estimation from experimental or lattice data. The extraction of low-energy constants (LECs) is guided by physical principles such as naturalness in a quantifiable way and various sources of uncertainty are included by the specification of Bayesian priors. Special issues for EFT parameter estimation are demonstrated using representative model problems, and a set of diagnostics is developed to isolate and resolve these issues. We apply the framework to the extraction of the LECs of the nucleon mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
Twistor Diagrams and Quantum Field Theory.
NASA Astrophysics Data System (ADS)
O'Donald, Lewis
Available from UMI in association with The British Library. Requires signed TDF. This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical view-point, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, 1990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sum-over -states idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various massless propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman "fish" diagrams of phi^4 -theory. However it is found that a more rigorous translation for the time-like fish requires new boundaries to be added to the twistor sum-over-states. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.
Radiative reactions in halo effective field theory
NASA Astrophysics Data System (ADS)
Rupak, Gautam
2016-03-01
In this article we review the recent progress in radiative reaction calculations in halo effective field theory. We look at radiative capture and breakup processes that involve a halo nucleus with a single valence neutron or proton. Looking at 7Li(n,γ) 8Li,14C(n,γ)15C and related reactions, the dominant source of theoretical uncertainty in s- and p-wave halo nuclei reaction calculations is quantified in a model-independent framework. The analysis for neutron halos is extended to proton halo systems. The effective field theory results quantify which observable parameters of the strong interaction at low energy need to be determined more precisely for accurate cross-section calculations.
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Quantum algorithms for quantum field theories
NASA Astrophysics Data System (ADS)
Jordan, Stephen
2015-03-01
Ever since Feynman's original proposal for quantum computers, one of the primary applications envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that quantum computers would be universal simulators, which can simulate all physical systems using computational resources that scale polynomially with the system's number of degrees of freedom. Quantum field theories have posed a challenge in that the set of degrees of freedom is formally infinite. We show how quantum computers, if built, could nevertheless efficiently simulate certain quantum field theories at bounded energy scales. Our algorithm includes a new state preparation technique which we believe may find additional applications in quantum algorithms. Joint work with Keith Lee and John Preskill.
Effective Field Theory for Lattice Nuclei
NASA Astrophysics Data System (ADS)
Barnea, N.; Contessi, L.; Gazit, D.; Pederiva, F.; van Kolck, U.
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at mπ≈800 MeV , we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states.
Effective field theory for lattice nuclei.
Barnea, N; Contessi, L; Gazit, D; Pederiva, F; van Kolck, U
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at m_{π}≈800 MeV, we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states. PMID:25699436
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Entanglement entropy in scalar field theory
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.
2013-01-01
Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here we perturbatively calculate the entanglement entropy in interacting scalar field theory, focusing on the dependence on the field’s mass. We study λϕ4 and gϕ3 theories in their ground state. By tracing over a half space, using the replica trick and position space Green’s functions on the cone, we show that spacetime volume divergences cancel and renormalization can be consistently performed in this conical geometry. We establish finite contributions to the entanglement entropy up to two-loop order, involving a finite area law. The resulting entropy is simple and intuitive: the free theory result in d = 3 (that we included in an earlier publication) ΔS ˜ A m2ln (m2) is altered, to leading order, by replacing the bare mass m by the renormalized mass mr evaluated at the renormalization scale of zero momentum.
Complete action for open superstring field theory
NASA Astrophysics Data System (ADS)
Kunitomo, Hiroshi; Okawa, Yuji
2016-02-01
We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is invariant under gauge transformations that are consistent with the projection for the string field in the Ramond sector.
Higher spin double field theory: a proposal
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Park, Jeong-Hyuck
2016-07-01
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Capture Reactions with Halo Effective Field Theory
NASA Astrophysics Data System (ADS)
Higa, R.
2015-12-01
Loosely bound nuclei far from the stability region emerge as a quantum phenomenon with many universal properties. The connection between these properties and the underlying symmetries can be best explored with halo/cluster EFT, an effective field theory where the softness of the binding momentum and the hardness of the core(s) form the expansion parameter of a given perturbative approach. In the following I highlight a particular application where these ideas are being tested, namely capture reactions.
Halo Effective Field Theory of 6He
NASA Astrophysics Data System (ADS)
Thapaliya, Arbin; Ji, Chen; Phillips, Daniel
2016-03-01
6He has a cluster structure with a tight 4He (α) core surrounded by two loosely bound neutrons (n) making it a halo nucleus. The leading-order (LO) Halo Effective Field Theory (EFT) [1, 2] calculations using momentum-space Faddeev equations pertinent to a bound 6He were carried out in [3]. In this work, we investigate 6He up to next-to-leading order (NLO) within Halo EFT.
Fundamentals of nonassociative classical field theory
Kurdgelaidze, D.F.
1987-05-01
A nonassociative classical field theory is constructed. Octonion algebra is studied. The octonion is represented as the sum of a quaternion and an associator. The octonion algebra is expanded and Lorentz group generators are specified in terms of octonion bases in one of the subalgebras. Lorentz vectors and spinors are constructed in the nonassociative algebra. The representation of the Lorentz group in terms of spin and the associator is obtained.
Closed string field theory from polyhedra
NASA Astrophysics Data System (ADS)
Saadi, Maha; Zwiebach, Barton
1989-05-01
A fully nonpolynomial framework for closed string field theory is studied. All interactions are geometrical, the pattern of string overlaps gives polyhedra with equal perimeter faces and three edges at each vertex. All interactions are cubic in the sense that at most three strings can coincide at a point. The three point vertex used is that of Witten which is seen to be quite natural in the framework of quadratic differentials and to induce a very symmetric decomposition of moduli space.
String theory, supergravity and four-dimensional field theories
NASA Astrophysics Data System (ADS)
Burrington, Benjamin A.
In this dissertation I present some of the basic computations in string theory and supergravity with an eye for their use in AdS/CFT. I then go on to present several investigations centering around the framework of dualities between gauge theory and gravity systems. In chapters 2, 3, and 4 we consider several 10D solutions. Chapter 2 deals with the inclusion of D7 branes in a D3 brane background, which amounts to adding fundamental matter in the gauge theory dual. We consider including the gravitational backreaction of the D7 branes in these solutions. In chapter 3, we consider modifications to the 6D space transverse to a stack of D3 branes. The 6D spaces that we consider are cones over the so called Y p,q geometries. We consider a geometric deformation for each of these spaces which explicitly breaks a U(1) isometry. In chapter 4, the leading Regge behavior string states are examined. We calculate the effective coupling of such string states to the five form and metric in a flat space background, and obtain an effective Lagrangian. Using this Lagrangian, we examine the energy, spin and angular momentum of these states in the AdS 5 x S5 background which is then compared to the semiclassical analysis of the literature. In chapters 5 and 6, we turn to discussions of the AdS5 factor. The Karch Randall scenario, a brane world scenario based oil AdS4 slices of AdS5 naturally suggests considering transparent boundary conditions for the field theory in AdS4. In chapter 5 we show that with these boundary conditions, a mass is induced for the graviphoton, and that this mass is in the correct proportion to the graviton mass (studied in the literature) to preserve supersymmetry. In chapter 6 we examine black hole solutions in AdS5. The presence of the black hole breaks some of the global supersymmetries (present in pure AdS5) which we use to generate the superpartners to these black holes. Using boundary counter term techniques, we find the mass, angular momentum, and charge
Backreacted axion field ranges in string theory
NASA Astrophysics Data System (ADS)
Baume, Florent; Palti, Eran
2016-08-01
String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter controlling the effective decay constant is unconstrained by tadpoles and can in principle lead to an arbitrarily large effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement leaving a sub-Planckian effective decay constant.
Gauge field theory of covariant strings
NASA Astrophysics Data System (ADS)
Kaku, Michio
1986-03-01
We present a gauge covariant second-quantized field theory of strings which is explicitly invariant under the gauge transformations generated by the Virasoro algebra. Unlike the old field theory strings [1] this new formulation is Lorentz covariant as well as gauge covariant under the continuous group Diff( S1) and its central extension. We derive the free action: L=Φ(X) †P[i∂ τ-(L 0-1)]PΦ(X) , in the same way that Feynman derived the Schrödinger equation from the path integral formalism. The action is manifestly invariant under the gauge transformation δΦ(X)= limit∑n=1∞ɛ -nL -nΦ(X) , where P is a projection operator which annihilates spurious states. We give three distinct formulations of this operator P to all orders, the first based on extracting the operator from the functional formulation of the Nambu-Goto action, and the second and third based on inverting the Shapovalov matrix on a Verma module. This gauge covariant formulation can be easily extended to the Green-Schwarz superstring [2,3]. One element application of these methods is to re-express the old Neveu-Schwarz-Ramond model as a field theory which is manifestly invariant under space-time supersymmetric transformations.
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Review of micro/nano technologies and theories for electroporation of biological cells
NASA Astrophysics Data System (ADS)
Lee, YiKuen; Deng, PeiGang
2012-06-01
Electroporation (EP) is one of the important techniques for the introduction of genes and drugs into cells with intense pulsed electric field to induce nanometer-sized electropores on cell membranes. Recently, micro/nano technology has been applied to many novel micro EP devices which can not only significantly increase uptake of biomolecules, DNA transfection and cell viability, but also enable large-scale single-cell EP. However, most EP theories developed in the past three decades can not precisely predict the experimental results of EP of biological cells. With the advanced micro EP chips for large-scale single-cell EP experiments, more precise EP theoretical models can be developed to describe the complicated multiscale dynamic behavior of EP.
Multiloop calculations in perturbative quantum field theory
NASA Astrophysics Data System (ADS)
Blokland, Ian Richard
This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for problems in a field of particle physics with a very rich history. The third calculation provides an improved prediction for the decay of a top quark. In order to obtain this result, a large class of multiloop integrals has been solved for the first time. Top quark decay is just one member of a family of interesting physical processes to which these new results apply. Since specialized calculational techniques are essential ingredients in all three calculations, they are motivated and explained carefully in this thesis. These techniques, once automated with symbolic computational software, have recently opened avenues of solution to a wide variety of important problems in particle physics.
Inhomogeneous field theory inside the arctic circle
NASA Astrophysics Data System (ADS)
Allegra, Nicolas; Dubail, Jérôme; Stéphan, Jean-Marie; Viti, Jacopo
2016-05-01
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point (Δ =0 ). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
On conformal field theories with extremal values
NASA Astrophysics Data System (ADS)
Zhiboedov, Alexander
2014-04-01
Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy tensor. We analyze energy correlators in parity invariant four-dimensional CFTs. The goal is to use the positivity of energy correlators to further constrain unitary CFTs. It is known that the positivity of the simplest one-point energy correlator implies that where a and c are the Weyl anomaly coefficients. We use the positivity of higher point energy correlators to show that CFTs with extremal values of have trivial scattering observables. More precisely, for and all energy correlators are fixed to be the ones of the free boson and the free vector theory correspondingly. Similarly, we show that the positivity and finiteness of energy correlators together imply that the three-point function of the stress tensor in a CFT cannot be proportional to the one in the theory of free boson, free fermion or free vector field.
Bayesian parameter estimation for effective field theories
NASA Astrophysics Data System (ADS)
Wesolowski, S.; Klco, N.; Furnstahl, R. J.; Phillips, D. R.; Thapaliya, A.
2016-07-01
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
The effective field theory of dark energy
NASA Astrophysics Data System (ADS)
Gubitosi, Giulia; Piazza, Federico; Vernizzi, Filippo
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Conformal field theories, representations and lattice constructions
NASA Astrophysics Data System (ADS)
Dolan, L.; Goddard, P.; Montague, P.
1996-07-01
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z 2-twisted theories, ℋ( Λ) andtilde H(Λ ) respectively, which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct latticesΛ _C andtilde Λ _C by analogous constructions from a doubly-even binary codeC. In the case whenC is self-dual, the corresponding lattices are also. Similarly, ℋ( Λ) andtilde H(Λ ) are self-dual if and only if Λ is. We show thatH(Λ _C ) has a natural “triality” structure, which induces an isomorphismH(tilde Λ _C ) ≡tilde H(Λ _C ) and also a triality structure ontilde H(tilde Λ _C ). ForC the Golay code,tilde Λ _C is the Leech lattice, and the triality ontilde H(tilde Λ _C ) is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories ℋ( Λ) andtilde H(Λ ) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.
Canonical quantization of Galilean covariant field theories
NASA Astrophysics Data System (ADS)
Santos, E. S.; de Montigny, M.; Khanna, F. C.
2005-11-01
The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein-Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term λΦ4. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron-electron and the electron-positron scattering. These examples show that the so-called 'non-relativistic' approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.
QCD unitarity constraints on Reggeon Field Theory
NASA Astrophysics Data System (ADS)
Kovner, Alex; Levin, Eugene; Lublinsky, Michael
2016-08-01
We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
Thermalization of Strongly Coupled Field Theories
Balasubramanian, V.; Bernamonti, A.; Copland, N.; Craps, B.; Staessens, W.; Boer, J. de; Keski-Vakkuri, E.; Mueller, B.; Schaefer, A.; Shigemori, M.
2011-05-13
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.
Thermalization of strongly coupled field theories.
Balasubramanian, V; Bernamonti, A; de Boer, J; Copland, N; Craps, B; Keski-Vakkuri, E; Müller, B; Schäfer, A; Shigemori, M; Staessens, W
2011-05-13
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first. PMID:21668141
Compact boson stars in K field theories
NASA Astrophysics Data System (ADS)
Adam, C.; Grandi, N.; Klimas, P.; Sánchez-Guillén, J.; Wereszczyński, A.
2010-11-01
We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.
Scalar-field theory of dark matter
NASA Astrophysics Data System (ADS)
Huang, Kerson; Xiong, Chi; Zhao, Xiaofei
2014-05-01
We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein-Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Drift estimation from a simple field theory
Mendes, F. M.; Figueiredo, A.
2008-11-06
Given the outcome of a Wiener process, what can be said about the drift and diffusion coefficients? If the process is stationary, these coefficients are related to the mean and variance of the position displacements distribution. However, if either drift or diffusion are time-dependent, very little can be said unless some assumption about that dependency is made. In Bayesian statistics, this should be translated into some specific prior probability. We use Bayes rule to estimate these coefficients from a single trajectory. This defines a simple, and analytically tractable, field theory.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
XXIVth International Symposium on Lattice Field Theory
NASA Astrophysics Data System (ADS)
2006-12-01
Lattice 2006, the XXIV International Symposium on Lattice Field Theory, was held from July 23-28, 2006 at the Starr Pass Hotel near Tucson, Arizona, USA, hosted by the University of Arizona Physics Department. The scientific program contained 25 plenary session talks and 193 parallel session contributions (talks and posters). Topics in lattice QCD included: hadron spectroscopy; hadronic interactions and structure; algorithms, machines, and networks; chiral symmetry; QCD confinement and topology; quark masses, gauge couplings, and renormalization; electroweak decays and mixing; high temperature and density; and theoretical developments. Topics beyond QCD included large Nc, Higgs, SUSY, gravity, and strings.
Pauli-Villars regulatization of supergravity and field theory anomalies
Gaillard, M.K.
1995-06-01
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
Towards a quantum field theory of primitive string fields
Ruehl, W.
2012-10-15
We denote generating functions of massless even higher-spin fields 'primitive string fields' (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher-spin field theories in AdS{sub d+1} are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 {<=} N {<=}{infinity} play for us the role of 'standard models', for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = {infinity}. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s {>=} 4, they are distinguished by their anomalous dimensions (in CFT{sub 3}) or by theirmass (in AdS{sub 4}). We sum over these multiplets and the spins to obtain 'string type fields', one for each such monomial.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
Conformal field theory of critical Casimir forces
NASA Astrophysics Data System (ADS)
Emig, Thorsten; Bimonte, Giuseppe; Kardar, Mehran
2015-03-01
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional conformal field theories (CFT) we derive exact results for the Casimir interaction for a deformed strip and for two compact objects of arbitrary shape in terms of the free energy of a standard region (circular ring or flat strip) whose dimension is determined by the mutual capacitance of two conductors with the objects' shape; and a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details. The effect of inhomogenous boundary conditions is also discussed.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Gauge gravitation theory: Gravity as a Higgs field
NASA Astrophysics Data System (ADS)
Sardanashvily, Gennadi
2016-05-01
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking, where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.
Ramond equations of motion in superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2015-11-01
We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Perfect magnetohydrodynamics as a field theory
Bekenstein, Jacob D.; Betschart, Gerold
2006-10-15
We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of ({Dirac_h}/2{pi}); this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Marginally Relevant Topics in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Cleary, Kevin Francis
We consider a set of topics in conformal field theory. We provide an example of a 4D theory that exhibits the Contino-Pomarol-Rattazzi mechanism, where breaking conformal symmetry by an almost marginal operator leads to a light pseudo-Goldstone boson, the dilaton, and a parametrically suppressed contribution to vacuum energy. We consider SUSY QCD at the edge of the conformal window and break conformal symmetry by weakly gauging a subgroup of the flavor symmetry. Using Seiberg duality we show that for a range of parameters the singlet meson in the dual theory reaches the unitarity bound, however, this theory does not have a stable vacuum. We stabilize the vacuum with soft breaking terms, compute the mass of the dilaton, and determine the range of parameters where the leading contribution to the dilaton mass is from the almost marginal coupling. We also weigh in on a widely held belief that increasing bounds on the gluino mass, which feeds down to the stop mass through renormalization group running, are making a light stop increasingly unlikely. Here we present a counter-example. We examine the case of the Minimal Composite Supersymmetric Standard Model which has a light composite stop. The large anomalous dimension of the stop from strong dynamics pushes the stop mass toward a quasi-fixed point in the infrared, which is smaller than standard estimates by a factor of a large logarithm. The gluino can be about three times heavier than the stop, which is comparable to hierarchy achieved with supersoft Dirac gluino masses. Thus, in this class of models, a heavy gluino is not necessarily indicative of a heavy stop.
Standard Model as a Double Field Theory.
Choi, Kang-Sin; Park, Jeong-Hyuck
2015-10-23
We show that, without any extra physical degree introduced, the standard model can be readily reformulated as a double field theory. Consequently, the standard model can couple to an arbitrary stringy gravitational background in an O(4,4) T-duality covariant manner and manifest two independent local Lorentz symmetries, Spin(1,3)×Spin(3,1). While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the standard model more rigid, and also stringy, than it appeared. The CP violating θ term may no longer be allowed by the symmetry, and hence the strong CP problem can be solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may belong to the two different spin classes. PMID:26551099
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Standard Model as a Double Field Theory
NASA Astrophysics Data System (ADS)
Choi, Kang-Sin; Park, Jeong-Hyuck
2015-10-01
We show that, without any extra physical degree introduced, the standard model can be readily reformulated as a double field theory. Consequently, the standard model can couple to an arbitrary stringy gravitational background in an O (4 ,4 ) T -duality covariant manner and manifest two independent local Lorentz symmetries, Spin(1 ,3 )×Spin(3 ,1 ) . While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the standard model more rigid, and also stringy, than it appeared. The C P violating θ term may no longer be allowed by the symmetry, and hence the strong C P problem can be solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may belong to the two different spin classes.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
2014-03-01
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Statistical field theory of a nonadditive system
NASA Astrophysics Data System (ADS)
Olemskoi, A. I.; Yushchenko, O. V.; Badalyan, A. Yu.
2013-03-01
Based on quantum field methods, we develop a statistical theory of complex systems with nonadditive potentials. Using the Martin-Siggia-Rose method, we find the effective system Lagrangian, from which we obtain evolution equations for the most probable values of the order parameter and its fluctuation amplitudes. We show that these equations are unchanged under deformations of the statistical distribution while the probabilities of realizing different phase trajectories depend essentially on the nonadditivity parameter. We find the generating functional of a nonadditive system and establish its relation to correlation functions; we introduce a pair of additive generating functionals whose expansion terms determine the set of multipoint Green's functions and their self-energy parts. We find equations for the generating functional of a system having an internal symmetry and constraints. In the harmonic approximation framework, we determine the partition function and moments of the order parameter depending on the nonadditivity parameter. We develop a perturbation theory that allows calculating corrections of an arbitrary order to the indicated quantities.
Multidimensional wave field signal theory: Mathematical foundations
NASA Astrophysics Data System (ADS)
Baddour, Natalie
2011-06-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Hamiltonian constraint in polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2011-01-15
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
Characterization of Pressure Transients Generated by Nanosecond Electrical Pulse (nsEP) Exposure
NASA Astrophysics Data System (ADS)
Roth, Caleb C.; Barnes, Ronald A., Jr.; Ibey, Bennett L.; Beier, Hope T.; Christopher Mimun, L.; Maswadi, Saher M.; Shadaram, Mehdi; Glickman, Randolph D.
2015-10-01
The mechanism(s) responsible for the breakdown (nanoporation) of cell plasma membranes after nanosecond pulse (nsEP) exposure remains poorly understood. Current theories focus exclusively on the electrical field, citing electrostriction, water dipole alignment and/or electrodeformation as the primary mechanisms for pore formation. However, the delivery of a high-voltage nsEP to cells by tungsten electrodes creates a multitude of biophysical phenomena, including electrohydraulic cavitation, electrochemical interactions, thermoelastic expansion, and others. To date, very limited research has investigated non-electric phenomena occurring during nsEP exposures and their potential effect on cell nanoporation. Of primary interest is the production of acoustic shock waves during nsEP exposure, as it is known that acoustic shock waves can cause membrane poration (sonoporation). Based on these observations, our group characterized the acoustic pressure transients generated by nsEP and determined if such transients played any role in nanoporation. In this paper, we show that nsEP exposures, equivalent to those used in cellular studies, are capable of generating high-frequency (2.5 MHz), high-intensity (>13 kPa) pressure transients. Using confocal microscopy to measure cell uptake of YO-PRO®-1 (indicator of nanoporation of the plasma membrane) and changing the electrode geometry, we determined that acoustic waves alone are not responsible for poration of the membrane.
Characterization of Pressure Transients Generated by Nanosecond Electrical Pulse (nsEP) Exposure
Roth, Caleb C.; Barnes Jr., Ronald A.; Ibey, Bennett L.; Beier, Hope T.; Christopher Mimun, L.; Maswadi, Saher M.; Shadaram, Mehdi; Glickman, Randolph D.
2015-01-01
The mechanism(s) responsible for the breakdown (nanoporation) of cell plasma membranes after nanosecond pulse (nsEP) exposure remains poorly understood. Current theories focus exclusively on the electrical field, citing electrostriction, water dipole alignment and/or electrodeformation as the primary mechanisms for pore formation. However, the delivery of a high-voltage nsEP to cells by tungsten electrodes creates a multitude of biophysical phenomena, including electrohydraulic cavitation, electrochemical interactions, thermoelastic expansion, and others. To date, very limited research has investigated non-electric phenomena occurring during nsEP exposures and their potential effect on cell nanoporation. Of primary interest is the production of acoustic shock waves during nsEP exposure, as it is known that acoustic shock waves can cause membrane poration (sonoporation). Based on these observations, our group characterized the acoustic pressure transients generated by nsEP and determined if such transients played any role in nanoporation. In this paper, we show that nsEP exposures, equivalent to those used in cellular studies, are capable of generating high-frequency (2.5 MHz), high-intensity (>13 kPa) pressure transients. Using confocal microscopy to measure cell uptake of YO-PRO®-1 (indicator of nanoporation of the plasma membrane) and changing the electrode geometry, we determined that acoustic waves alone are not responsible for poration of the membrane. PMID:26450165
Characterization of Pressure Transients Generated by Nanosecond Electrical Pulse (nsEP) Exposure.
Roth, Caleb C; Barnes, Ronald A; Ibey, Bennett L; Beier, Hope T; Christopher Mimun, L; Maswadi, Saher M; Shadaram, Mehdi; Glickman, Randolph D
2015-01-01
The mechanism(s) responsible for the breakdown (nanoporation) of cell plasma membranes after nanosecond pulse (nsEP) exposure remains poorly understood. Current theories focus exclusively on the electrical field, citing electrostriction, water dipole alignment and/or electrodeformation as the primary mechanisms for pore formation. However, the delivery of a high-voltage nsEP to cells by tungsten electrodes creates a multitude of biophysical phenomena, including electrohydraulic cavitation, electrochemical interactions, thermoelastic expansion, and others. To date, very limited research has investigated non-electric phenomena occurring during nsEP exposures and their potential effect on cell nanoporation. Of primary interest is the production of acoustic shock waves during nsEP exposure, as it is known that acoustic shock waves can cause membrane poration (sonoporation). Based on these observations, our group characterized the acoustic pressure transients generated by nsEP and determined if such transients played any role in nanoporation. In this paper, we show that nsEP exposures, equivalent to those used in cellular studies, are capable of generating high-frequency (2.5 MHz), high-intensity (>13 kPa) pressure transients. Using confocal microscopy to measure cell uptake of YO-PRO®-1 (indicator of nanoporation of the plasma membrane) and changing the electrode geometry, we determined that acoustic waves alone are not responsible for poration of the membrane. PMID:26450165
Greg Beshouri; Kirby S. Chapman; Jim McCarthy; Sarah R. Nuss-Warren; Mike Whelan
2006-03-01
This quarterly report re-evaluates current market objectives in the exploration and production industry, discusses continuing progress in testing that evaluates emission control technologies applied to a two-stroke cycle natural gas-fueled engine, and presents a scheme for enacting remote monitoring and control of engines during upcoming field tests. The examination of current market objectives takes into account technological developments and changing expectations for environmental permitting which may have occurred over the last year. This demonstrates that the continuing work in controlled testing and toward field testing is on track Market pressures currently affecting the gas exploration and production industry are shown to include a push for increased production, as well as an increasing cost for environmental compliance. This cost includes the direct cost of adding control technologies to field engines as well as the indirect cost of difficulty obtaining permits. Environmental regulations continue to require lower emissions targets, and some groups of engines which had not previously been regulated will be required to obtain permits in the future. While the focus remains on NOx and CO, some permits require reporting of additional emissions chemicals. Continuing work in controlled testing uses a one cylinder Ajax DP-115 (a 13.25 in bore x 16 in stroke, 360 rpm engine) to assess a sequential analysis and evaluation of a series of engine upgrades. As with most of the engines used in the natural gas industry, the Ajax engine is a mature engine with widespread usage throughout the gas gathering industry. The end point is an assessment of these technologies that assigns a cost per unit reduction in NOx emissions. Technologies including one pre-combustion chamber, in-cylinder sensors, the means to adjust the air-to-fuel ratio, and modification of the air filter housing have been evaluated in previous reports. Current work focuses on final preparations for testing
Kirby S. Chapman; Sarah R. Nuss-Warren
2006-07-01
Continuing work in controlled testing uses a one cylinder Ajax DP-115 (a 13.25 in bore x 16 in stroke, 360 rpm engine) to assess a sequential analysis and evaluation of a series of engine upgrades. As with most of the engines used in the natural gas industry, the Ajax engine is a mature engine with widespread usage throughout the gas gathering industry. The end point is an assessment of these technologies that assigns a cost per unit reduction in NOX emissions. Technologies including one pre-combustion chamber, in-cylinder sensors, the means to adjust the air-to-fuel ratio, and modification of the air filter housing have been evaluated in previous reports. Current work focuses on final preparations for testing pre-combustion chambers with different characteristics and using mid-to-high-pressure fuel valves and initial runs of these tests. By using the Ajax DP-115 these tests are completed in a low-cost and efficient manner. The various technologies can be quickly exchanged with different hardware, and it is inexpensive to run the engine. Progress in moving toward field testing is discussed, and changes to the first planned field test are presented. Although changes have been made to the previous plan, it is expected that several new sites will be selected soon. Field tests will begin in the next quarter.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Intracardiac electrophysiology study (EPS)
... called catheter ablation ) Watch this video about: Cardiac conduction system How to Prepare for the Test You ... study - intracardiac; EPS - intracardiac Images Heart, front view Conduction system of the heart References Miller JM, Zipes ...
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Quarkonium hybrids with nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Berwein, Matthias; Brambilla, Nora; Tarrús Castellà, Jaume; Vairo, Antonio
2015-12-01
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass m of the heavy quark. At order 1 /m in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as Λ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for c c ¯, b c ¯, and b b ¯ hybrids. The Λ -doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.
Effective Field Theory for Rydberg Polaritons
NASA Astrophysics Data System (ADS)
Gullans, M. J.; Wang, Y.; Thompson, J. D.; Liang, Q.-Y.; Vuletic, V.; Lukin, M. D.; Gorshkov, A. V.
2016-05-01
Photons can be made to strongly interact by dressing them with atomic Rydberg states under conditions of electromagnetic induced transparency. Probing Rydberg polaritons in the few-body limit, recent experiments were able to observe non-perturbative two-body effects including: single photon switching and the formation of bound states. Although the two-body problem is amenable to exact solutions, such approaches quickly become intractable for more than two particles. To overcome this problem, we study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). For attractive interactions, we show how a suitably long medium can be used to prepare shallow N-body bound states in one dimension. We verify this prediction for two and three photons using full numerical simulations. We then consider conditions under which the effective interactions are repulsive and study two and three photon transmission. Finally, we show how to go beyond EFT by measuring the three-body contact force or, alternatively, scattering at high relative momenta.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (
Superconformal field theory and Jack superpolynomials
NASA Astrophysics Data System (ADS)
Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2012-09-01
We uncover a deep connection between the {N} = {1} superconformal field theory in 2 D and eigenfunctions of the supersymmetric Sutherland model known as Jack super-polynomials (sJacks). Specifically, the singular vector at level rs/2 of the Kac module labeled by the two integers r and s are given explicitly as a sum of sJacks whose indexing diagrams are contained in a rectangle with r columns and s rows. As a second compelling evidence for the distinguished status of the sJack-basis in SCFT, we find that the degenerate Whittaker vectors (Gaiotto states) can be expressed as a remarkably simple linear combination of sJacks. As a consequence, we are able to reformulate the supersymmetric version of the (degenerate) AGT conjecture in terms of the combinatorics of sJacks. The closed-form formulas for the singular vectors and the degenerate Whittaker vectors, although only conjectured in general, have been heavily tested (in some cases, up to level 33/2). Both the Neveu-Schwarz and Ramond sectors are treated.
Cluster Mass Inference via Random Field Theory
Zhang, Hui; Nichols, Thomas E.; Johnson, Timothy D.
2009-01-01
Cluster extent and voxel intensity are two widely used statistics in neuroimaging inference. Cluster extent is sensitive to spatially extended signals while voxel intensity is better for intense but focal signals. In order to leverage strength from both statistics, several nonparametric permutation methods have been proposed to combine the two methods. Simulation studies have shown that of the different cluster permutation methods, the cluster mass statistic is generally the best. However, to date, there is no parametric cluster mass inference method available. In this paper, we propose a cluster mass inference method based on random field theory (RFT). We develop this method for Gaussian images, evaluate it on Gaussian and Gaussianized t-statistic images and investigate its statistical properties via simulation studies and real data. Simulation results show that the method is valid under the null hypothesis and demonstrate that it can be more powerful than the cluster extent inference method. Further, analyses with a single-subject and a group fMRI dataset demonstrate better power than traditional cluster extent inference, and good accuracy relative to a gold-standard permutation test. PMID:18805493
Logarithmic conformal field theory: a lattice approach
NASA Astrophysics Data System (ADS)
Gainutdinov, A. M.; Jacobsen, J. L.; Read, N.; Saleur, H.; Vasseur, R.
2013-12-01
Logarithmic conformal field theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self-avoiding walks, etc), or of critical points in several classes of disordered systems (transition between plateaux in the integer and spin quantum Hall effects). Much progress in their understanding has been obtained by studying algebraic features of their lattice regularizations. For reasons which are not entirely understood, the non-semi-simple associative algebras underlying these lattice models—such as the Temperley-Lieb algebra or the blob algebra—indeed exhibit, in finite size, properties that are in full correspondence with those of their continuum limits. This applies not only to the structure of indecomposable modules, but also to fusion rules, and provides an ‘experimental’ way of measuring couplings, such as the ‘number b’ quantifying the logarithmic coupling of the stress-energy tensor with its partner. Most results obtained so far have concerned boundary LCFTs and the associated indecomposability in the chiral sector. While the bulk case is considerably more involved (mixing in general left and right moving sectors), progress has also recently been made in this direction, uncovering fascinating structures. This study provides a short general review of our work in this area.
Next-to-simplest quantum field theories
NASA Astrophysics Data System (ADS)
Lal, Shailesh; Raju, Suvrat
2010-05-01
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
Next-to-simplest quantum field theories
Lal, Shailesh; Raju, Suvrat
2010-05-15
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
NASA Astrophysics Data System (ADS)
Zatloukal, Václav
2016-04-01
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.
Mean field theory for long chain molecules
NASA Astrophysics Data System (ADS)
Pereira, Gerald G.
1996-06-01
We provide a mathematical formalism for a self-consistent mean field treatment of long chain molecules. The formalism is applied to the case of a neutral polymer under the excluded volume interaction. Upon scaling the problem in the N→∞ limit we find the natural scaling length RN, of the polymer, which is made up of (N+1) monomers or beads, is RN˜N3/5, the well known Flory result. The asymptotics of the problem is dominated by the neighborhood of the turning point, so that a uniformly valid Green's function solution of the differential equations is necessary. In the neighborhood of a point y* the scaled polymer density fN(x), is found to decay sharply. If we let x denote the scaled distance from one end of the chain to a point in space we obtain, for y*-x≳O(N-2/15), a closed form expression for the polymer density viz., fN(x)˜{1/2x2[fN(x)-fN(y*)]1/2} while for x-y*≳O(N-2/15) the density is shown to be, to leading order, zero. Although our results imply the rate of decay of the density at y* is O(N1/5) we are unable to verify this explicitly by calculating fN'(y*). We believe this is due to the inability of the WKB theory to correctly approximate solutions in regions of rapid variation. We suggest remedies for this, so that a complete self-consistent solution may be obtained.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
Effective field theory of broken spatial diffeomorphisms
NASA Astrophysics Data System (ADS)
Lin, Chunshan; Labun, Lance Z.
2016-03-01
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.
Multiscale quantum simulation of quantum field theory using wavelets
NASA Astrophysics Data System (ADS)
Brennen, Gavin K.; Rohde, Peter; Sanders, Barry C.; Singh, Sukhwinder
2015-09-01
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis—a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Reggeon Field Theory and the phases of QCD
White, A.R.
1987-07-21
We propose a Reggeon Field Theory phase diagram involving Sub-critical and Super-critical Pomeron behavior and the Expanding Disc. We describe the derivation of Reggeon Field Theory from QCD using infra-red analysis of the reggeon diagrams of the spontaneously broken theory. Matching the Reggeon Field Theory phase-diagram to that of lattice QCD with many fermions has significant implications for the chiral properties of continuum QCD when the number of flavors is less than the maximum allowed by asymptotic freedom. 19 refs., 7 figs.
Electroweak Sudakov Corrections using Effective Field Theory
Chiu Juiyu; Golf, Frank; Kelley, Randall; Manohar, Aneesh V.
2008-01-18
Electroweak Sudakov corrections of the form {alpha}{sup n}log{sup m}s/M{sub W,Z}{sup 2} are summed using renormalization group evolution in soft-collinear effective theory. Results are given for the scalar, vector, and tensor form factors for fermion and scalar particles. The formalism for including massive gauge bosons in soft-collinear effective theory is developed.
NS-NS sector of closed superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2014-08-01
We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.
Effective field theory: A modern approach to anomalous couplings
Degrande, Céline; Centre for Particle Physics and Phenomenology , Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve ; Greiner, Nicolas; Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München ; Kilian, Wolfgang; University of Siegen, Fachbereich Physik, D-57068 Siegen ; Mattelaer, Olivier; Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott; Zhang, Cen; Centre for Particle Physics and Phenomenology , Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve
2013-08-15
We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics.
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Nonlocal Stochastic Model for the Free Scalar Field Theory
NASA Astrophysics Data System (ADS)
Namsrai, Kh.
1981-05-01
The free scalar field is investigated within the framework of the Davidson stochastic model and of the hypothesis on space-time stochasticity. It is shown that the resulting Markov field obtained by averaging in this space-time is equivalent to a nonlocal Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter ν. Our result generalizes Guerra and Ruggiero's procedure of stochastic quantization of scalar fields. On the basis of the assumption about unobservability of ν in quantum field theory, the Efimov nonlocal theory is obtained from Euclidean Markov field with form factors of the class of entire analytical functions.
Comparisons and connections between mean field dynamo theory and accretion disc theory
NASA Astrophysics Data System (ADS)
Blackman, E. G.
2010-01-01
The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Field Theory Model of the Flyby Anomaly
Lewis, R. A
2009-03-16
Precision tracking of spacecraft on interplanetary missions has turned up several anomalous deviations from predictions of general relativity. The Flyby Anomaly, wherein spacecraft gain or lose energy in an earth-centric frame after an encounter with earth, is clearly associated with the rotation of the earth. The possibility that the missing ingredient is a new type of potential field surrounding the earth is assessed in this write-up. A scalar field with the kinetic energy distribution of the earth as a source is evaluated numerically, with an amplitude parameter adjusted to match the data of Anderson et al.(2008). The new field can be interpreted as a coupling between kinetic energies of objects, a field analogous to fluid mechanics, or a field coupled to acceleration. The potential field violates various aspects of standard physics, such as energy non-conservation.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Open superstring field theory on the restricted Hilbert space
NASA Astrophysics Data System (ADS)
Konopka, Sebastian; Sachs, Ivo
2016-04-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Lorentz symmetric quantum field theory for symplectic fermions
Robinson, Dean J.; Kapit, Eliot; LeClair, Andre
2009-11-15
A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a Klein-Gordon Lagrangian. This theory is shown to have all the required properties of a consistent free quantum field theory, namely, causality, unitarity, adherence to the spin-statistics theorem, CPT symmetry, and the Hermiticity and positive definiteness of the Hamiltonian. The global symmetry of the free theory is Sp(4){approx_equal}SO(5). Possible interacting theories of both the pseudo-Hermitian and Hermitian variety are then examined briefly.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
Lorentz symmetry breaking as a quantum field theory regulator
NASA Astrophysics Data System (ADS)
Visser, Matt
2009-07-01
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just “how much” Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Hořava’s recent article [Phys. Rev. DPRVDAQ1550-7998 79, 084008 (2009)10.1103/PhysRevD.79.084008] on 3+1 dimensional quantum gravity.
Applying Power Theories to Field Settings.
ERIC Educational Resources Information Center
Liss, Lora
To test theories presented in the sociology course "Social Policies and Community Power Structure," a team of undergraduate students and their instructor attended a national professional conference. The following are examples of those concepts the students observed in operation at the conference: Social structure affects social policies; the…
A class of effective field theory models of cosmic acceleration
NASA Astrophysics Data System (ADS)
Bloomfield, Jolyon K.; Flanagan, Éanna É.
2012-10-01
We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Fermionic field theory for trees and forests.
Caracciolo, Sergio; Jacobsen, Jesper Lykke; Saleur, Hubert; Sokal, Alan D; Sportiello, Andrea
2004-08-20
We prove a generalization of Kirchhoff's matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a q-->0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that this latter model can be mapped, to all orders in perturbation theory, onto the N-vector model at N=-1 or, equivalently, onto the sigma model taking values in the unit supersphere in R(1|2). It follows that, in two dimensions, this fermionic model is perturbatively asymptotically free. PMID:15447166
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Killing vector fields and harmonic superfield theories
NASA Astrophysics Data System (ADS)
Groeger, Josua
2014-09-01
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
Statistical field theories deformed within different calculi
NASA Astrophysics Data System (ADS)
Olemskoi, A. I.; Borysov, S. S.; Shuda, I. A.
2010-09-01
Within the framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis and generalized by Naudts, we develop field-theoretical schemes of statistically distributed fields. We construct a set of generating functionals and find their connection with corresponding correlators for basic-deformed, finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of additive functionals, which expansions into deformed series yield both Green functions and their irreducible proper vertices. We find as well formal equations, governing by the generating functionals of systems which possess a symmetry with respect to a field variation and are subjected to an arbitrary constrain. Finally, we generalize field-theoretical schemes inherent in concrete calculi in the Naudts manner. From the physical point of view, we study dependences of both one-site partition function and variance of free fields on deformations. We show that within the basic-deformed statistics dependence of the specific partition function on deformation has in logarithmic axes symmetrical form with respect to maximum related to deformation absence; in case of the finite-difference statistics, the partition function takes non-deformed value; for the Kaniadakis statistics, curves of related dependences have convex symmetrical form at small curvatures of the effective action and concave form at large ones. We demonstrate that only moment of the second order of free fields takes non-zero values to be proportional to inverse curvature of effective action. In dependence of the deformation parameter, the free field variance has linearly arising form for the basic-deformed distribution and increases non-linearly rapidly in case of the finite-difference statistics; for more complicated case of the Kaniadakis distribution, related dependence has double-well form.
New class of effective field theories from embedded branes.
Goon, Garrett L; Hinterbichler, Kurt; Trodden, Mark
2011-06-10
We present a new general class of four-dimensional effective field theories with interesting global symmetry groups. These theories arise from purely gravitational actions for (3+1)-dimensional branes embedded in higher dimensional spaces with induced gravity terms. The simplest example is the well known Galileon theory, with its associated Galilean symmetry, arising as the limit of a DGP brane world. However, we demonstrate that this is a special case of a much wider range of theories, with varying structures, but with the same attractive features such as second order equations. In some circumstances, these new effective field theories allow potentials for the scalar fields on curved space, with small masses protected by nonlinear symmetries. Such models may prove relevant to the cosmology of both the early and late universe. PMID:21770494
Using Self Consistent Field Theory on Polymeric Mixtures
NASA Astrophysics Data System (ADS)
von Konigslow, Kier; Park, Chul; Thompson, Russell
The ability to predict the solubility of a particular solvent in a polymer fluid is essential to the production of polymer foams. For the past 40 years, the primary model employed to this end has been an expansion of Flory-Huggins lattice fluid theory developed by Sanchez and Lacombe (S-L theory). S-L theory, while useful in the uniform limit, is limited to homogeneous systems. Self-Consistent Field Theory (SCFT), which has long been in use in polymer physics, is a mean-field theory capable of modeling the equilibrium behaviour of both homogeneous and inhomogeneous systems. We are investigating whether SCFT, applied to polymer-solvent mixtures, is in agreement with SL-theory in the homogeneous limit. Should this prove successful, we hope to use SCFT to model more general mixtures, including inhomogeneous nanocellular polymer foam systems.
On the global symmetries of 6D superconformal field theories
NASA Astrophysics Data System (ADS)
Bertolini, Marco; Merkx, Peter R.; Morrison, David R.
2016-07-01
We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
Lattice Study of Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
Winterowd, Christopher; Detar, Carleton; Zafeiropoulos, Savvas
2016-03-01
The discovery of graphene ranks as one of the most important developments in condensed matter physics in recent years. As a strongly interacting system whose low-energy excitations are described by the Dirac equation, graphene has many similarities with other strongly interacting field theories, particularly quantum chromodynamics (QCD). Graphene, along with other relativistic field theories, have been predicted to exhibit spontaneous symmetry breaking (SSB) when an external magnetic field is present. Using nonperturbative methods developed to study QCD, we study the low-energy effective field theory (EFT) of graphene subject to an external magnetic field. We find strong evidence supporting the existence of SSB at zero-temperature and characterize the dependence of the chiral condensate on the external magnetic field. We also present results for the mass of the Nambu-Goldstone boson and the dynamically generated quasiparticle mass that result from the SSB.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
Fractal tracer distributions in turbulent field theories
NASA Astrophysics Data System (ADS)
Hansen, Jonas Lundbek; Bohr, Tomas
1998-07-01
We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and thereby find a regime in which the particle distribution is a strange attractor. We compare the Lyapunov dimension to the information dimension of actual particle distributions and show that there is good agreement with the Kaplan-Yorke conjecture. Similar phenomena have been observed experimentally.
Holographic thermal field theory on curved spacetimes
NASA Astrophysics Data System (ADS)
Marolf, Donald; Rangamani, Mukund; Wiseman, Toby
2014-03-01
The AdS/CFT correspondence relates certain strongly-coupled CFTs with large effective central charge ceff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly-coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma-balls, which become stable at large ceff. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame.
On-Shell Recursion Relations for Effective Field Theories.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2016-01-29
We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible. PMID:26871321
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
An extremal ${\\mathcal{N}}=2$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiral ${\\mathcal{N}}$ = 2 superconformal field theory at c = 24. The construction is based on a ${{\\mathbb{Z}}}_{2}$ orbifold of the theory associated to the ${A}_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.
Advances in reversed field pinch theory and computation
Schnack, D.D.; Ho, Y.L.; Carreras, B.A.; Sidikman, K.; Craddock, G.G.; Mattor, N.; Nebel, R.A.; Prager, S.C.; Terry, P.W.; Zita, E.J.
1992-12-31
Advances in theory and computations related to the reversed field pinch (RFP) are presented. These are: (1) the effect of the dynamo on thermal transport; (2) a theory of ion heating due to dynamo fluctuations; (3) studies of active and passive feedback schemes for controlling dynamo fluctuations; and (4) an analytic model for coupled g-mode and rippling turbulence in the RFP edge.
An extremal $${\\mathcal{N}}=2$$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiralmore » $${\\mathcal{N}}$$ = 2 superconformal field theory at c = 24. The construction is based on a $${{\\mathbb{Z}}}_{2}$$ orbifold of the theory associated to the $${A}_{1}^{24}$$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.« less
Theory of a quantum noncanonical field in curved spacetimes
Indurain, Javier; Liberati, Stefano
2009-08-15
Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from special relativity in the form of a deformed Poincare algebra. These proposals go generically under the name of doubly or deformed special relativity (DSR). In this article we further explore a recently proposed class of quantum field theories, involving noncanonically commuting complex scalar fields, which have been shown to entail a DSR-like symmetry. An open issue for such theories is whether the DSR-like symmetry has to be taken as a physically relevant symmetry, or if in fact the 'true' symmetries of the theory are just rotations and translations while boost invariance has to be considered broken. Here we analyze this issue by extending the known results to curved spacetime under both of the previous assumptions. We show that if the symmetry of the free theory is taken to be a DSR-like realization of the Poincare symmetry, then it is not possible to render such a symmetry a gauge symmetry of the curved physical spacetime. However, it is possible to introduce an auxiliary spacetime which allows one to describe the theory as a standard quantum field theory in curved spacetime. Alternatively, taking the point of view that the noncanonical commutation of the fields actually implies a breakdown of boost invariance, the physical spacetime manifold has to be foliated in surfaces of simultaneity, and the field theory can be coupled to gravity by making use of the Arnowitt-Deser-Misner prescription.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Topological field theory amplitudes for A N-1 fibration
NASA Astrophysics Data System (ADS)
Iqbal, Amer; Khan, Ahsan Z.; Qureshi, Babar A.; Shabbir, Khurram; Shehper, Muhammad A.
2015-12-01
We study the partition function N=1 5D U( N) gauge theory with g adjoint hypermultiplets and show that for massless adjoint hypermultiplets it is equal to the partition function of a two dimensional topological field on a genus g Riemann surface. We describe the topological field theory by its amplitudes associated with cap, propagator and pair of pants. These basic amplitudes are open topological string amplitudes associated with certain Calabi-Yau threefolds in the presence of Lagrangian branes.
Central charge bounds in 4D conformal field theory
Rattazzi, Riccardo; Vichi, Alessandro; Rychkov, Slava
2011-02-15
We derive model-independent lower bounds on the stress tensor central charge C{sub T} in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C{sub T} is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.
Non-perturbative methods in relativistic field theory
Franz Gross
2013-03-01
This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.
Effective field theory from modified gravity with massive modes
NASA Astrophysics Data System (ADS)
Capozziello, Salvatore; de Laurentis, Mariafelicia; Paolella, Mariacristina; Ricciardi, Giulia
2015-10-01
Massive gravitational modes in effective field theories can be recovered by extending General Relativity and taking into account generic functions of the curvature invariants, not necessarily linear in the Ricci scalar R. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed.
On the entanglement between interacting scalar field theories
NASA Astrophysics Data System (ADS)
Mozaffar, M. Reza Mohammadi; Mollabashi, Ali
2016-03-01
We study "field space entanglement" in certain quantum field theories consisting of N number of free scalar fields interacting with each other via kinetic mixing terms. We present exact analytic expressions for entanglement and Renyi entropies between arbitrary numbers of scalar fields by which we could explore certain entanglement inequalities. Other entanglement measures such as mutual information and entanglement negativity have also been studied. We also give some comments about possible holographic realizations of such models.
Quantum theory for plasmon-assisted local field enhancement
NASA Astrophysics Data System (ADS)
Grigorenko, Ilya
2016-01-01
We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.
Quantum theory for plasmon-assisted local field enhancement
NASA Astrophysics Data System (ADS)
Grigorenko, Ilya
We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.
Black holes from generalized gauge field theories
NASA Astrophysics Data System (ADS)
Diaz-Alonso, J.; Rubiera-Garcia, D.
2011-02-01
We summarize the main results of a broad analysis on electrostatic, spherically symmetric (ESS) solutions of a class of non-linear electrodynamics models minimally coupled to gravitation. Such models are defined as arbitrary functions of the two quadratic field invariants, constrained by several physical admissibility requirements, and split into different families according to the behaviour of these lagrangian density functions in vacuum and on the boundary of their domains of definition. Depending on these behaviours the flat-space energy of the ESS field can be finite or divergent. For each model we qualitatively study the structure of its associated gravitational configurations, which can be asymptotically Schwarzschild-like or with an anomalous non Schwarzschild-like behaviour at r → ∞ (but being asymptotically flat and well behaved anyhow). The extension of these results to the non-abelian case is also briefly considered.
Effective hydrodynamic field theory and condensation picture of topological insulators
NASA Astrophysics Data System (ADS)
Chan, AtMa P. O.; Kvorning, Thomas; Ryu, Shinsei; Fradkin, Eduardo
2016-04-01
While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac boundary spectrum, it remains elusive to develop a hydrodynamic or collective description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a U (1 ) gauge field that arises by gauging the continuous symmetry of the target system [the U (1 ) particle number conservation]. Integrating over the U (1 ) gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the U (1 ) gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description of the surface of topological insulators and the implication of its duality are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.
Quantum field theory of interacting plasmon-photon-phonon system
NASA Astrophysics Data System (ADS)
Hieu Nguyen, Van; Nguyen, Bich Ha
2015-09-01
This work is devoted to the construction of the quantum field theory of the interacting system of plasmons, photons and phonons on the basis of general fundamental principles of electrodynamics and quantum field theory of many-body systems. Since a plasmon is a quasiparticle appearing as a resonance in the collective oscillation of the interacting electron gas in solids, the starting point is the total action functional of the interacting system comprising electron gas, electromagnetic field and phonon fields. By means of the powerful functional integral technique, this original total action is transformed into that of the system of the quantum fields describing plasmons, transverse photons, acoustic as well as optic longitudinal and transverse phonons. The collective oscillations of the electron gas is characterized by a real scalar field φ(x) called the collective oscillation field. This field is split into the static background field φ0(x) and the fluctuation field ζ(x). The longitudinal phonon fields {{{Q}}al}(x), {{{Q}}ol}(x) are also split into the background fields {Q}0al(x), {Q}0ol(x) and dynamical fields {{{q}}al}(x), {{{q}}ol}(x) while the transverse phonon fields {{{Q}}at}(x), {{{Q}}ot}(x) themselves are dynamical fields {{{q}}at}(x), {{{q}}ot}(x) without background fields. After the canonical quantization procedure, the background fields φ0(x), {Q}0al(x), {Q}0ol(x) remain the classical fields, while the fluctuation fields ζ(x) and dynamical phonon fields {{{q}}al}(x), {{{q}}at}(x), {{{q}}ol}(x), {{{q}}ot}(x) become quantum fields. In quantum theory, a plasmon is the quantum of Hermitian scalar field σ(x) called the plasmon field, longitudinal phonons as complex spinless quasiparticles are the quanta of the effective longitudinal phonon Hermitian scalar fields {{θ }a}(x), {{θ }0}(x), while transverse phonons are the quanta of the original Hermitian transverse phonon vector fields {{{q}}at}(x), {{{q}}ot}(x). By means of the functional integral
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Fundamental string solutions in open string field theories
Michishita, Yoji
2006-02-15
In Witten's open cubic bosonic string field theory and Berkovits' superstring field theory we investigate solutions of the equations of motion with appropriate source terms, which correspond to Callan-Maldacena solution in Born-Infeld theory representing fundamental strings ending on the D-branes. The solutions are given in order by order manner, and we show some full order properties in the sense of {alpha}{sup '} expansion. In superstring case we show that the solution is 1/2 BPS in full order.
Mean Field Theory for Nonequilibrium Network Reconstruction
NASA Astrophysics Data System (ADS)
Roudi, Yasser; Hertz, John
2011-01-01
There has been recent progress on inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for nonequilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically coupled, synchronously updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one-time-step-delayed correlation functions.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Continuum regularization of quantum field theory
Bern, Z.
1986-01-01
Breit, Gupta, and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the fifth-time of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, difficulties arise which, in general, ruins the scheme. A successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest.
Generalization of the theory of far-field caustics by the catastrophe theory.
Theocaris, P S; Michopoulos, J G
1982-03-15
To generalize the theory of far-field caustics, three theorems and several corollaries are presented in this paper. Using the law of reflection and catastrophe theory we have established conditions to predict caustic patterns in a 3-D space, which were created from the reflection of a light beam from an analytically known surface. The general theory was readily reduced to the already known cases of diffraction, indicating the validity of the general theory. Experimental evidence in two simple cases of reflectors, consisting of triangular and rectangular membranes, corroborated the results of the theory. PMID:20389809
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
Effective Field Theories from Soft Limits of Scattering Amplitudes.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist. PMID:26196613
EPS (Electric Particulate Suspension) Microgravity Technology Provides NASA with New Tools
NASA Technical Reports Server (NTRS)
Colver, Gerald M.; Greene, Nate; Xu, Hua
2004-01-01
The Electric Particulate Suspension is a fire safety ignition test system being developed at Iowa State University with NASA support for evaluating combustion properties of powders, powder-gas mixtures, and pure gases in microgravity and gravitational atmospheres (quenching distance, ignition energy, flammability limits). A separate application is the use of EPS technology to control heat transfer in vacuum and space environment enclosures. In combustion testing, ignitable powders (aluminum, magnesium) are introduced in the EPS test cell and ignited by spark, while the addition of inert particles act as quenching media. As a combustion research tool, the EPS method has potential as a benchmark design for quenching powder flames that would provide NASA with a new fire safety standard for powder ignition testing. The EPS method also supports combustion modeling by providing accurate measurement of flame-quenching distance as an important parameter in laminar flame theory since it is closely related to characteristic flame thickness and flame structure. In heat transfer applications, inert powder suspensions (copper, steel) driven by electric fields regulate heat flow between adjacent surfaces enclosures both in vacuum (or gas) and microgravity. This simple E-field control can be particularly useful in space environments where physical separation is a requirement between heat exchange surfaces.
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
Emergent geometry from field theory: Wilson's renormalization group revisited
NASA Astrophysics Data System (ADS)
Kim, Ki-Seok; Park, Chanyong
2016-06-01
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low-energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdSd +2 /CFTd +1 duality conjecture. We claim that the AdS3 /CFT2 duality may be interpreted as Landau-Ginzburg theory combined with Wilson's renormalization group, which introduces vertex corrections into the Landau-Ginzburg theory in the large-Ns limit, where Ns is the number of fermion flavors.
The field theory of intersecting D3-branes
NASA Astrophysics Data System (ADS)
Mintun, Eric; Polchinski, Joseph; Sun, Sichun
2015-08-01
We examine the defect gauge theory on two perpendicular D3-branes with a 1+1 dimensional intersection, consisting of U(1) fields on the D3-branes and charged hypermultiplets on the intersection. We argue that this gauge theory must have a magnetically charged soliton corresponding to the D-string stretched between the branes. We show that the hypermultiplets actually source magnetic as well as electric fields. The magnetic charges are confined if the hypermultiplet action is canonical, but considerations of periodicity of the hypermultiplet space in string theory imply a nontrivial Gibbons-Hawking metric, and we show that there is then the expected magnetic kink solution. The hypermultiplet metric has a singularity, which we argue must be resolved by embedding in the full string theory. Another interesting feature is that the classical field equations have logarithmic divergences at the intersection, which lead to a classical renormalization group flow in the action.
Some equivalences between the auxiliary field method and envelope theory
Buisseret, Fabien; Semay, Claude; Silvestre-Brac, Bernard
2009-03-15
The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles a priori. This equivalence leads to a deeper understanding of both frameworks.
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
Hermeneutical Field Theory and the Structural Character of Understanding.
NASA Astrophysics Data System (ADS)
Whitehouse, William Leonard
Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints and degrees of freedom that constitute the structural character of understanding. However, as is sometimes the case with their quantitative mathematical counterparts, the hermeneutical field equations are capable of giving a variety of descriptions or solutions for one and the same set of conditions. The task, therefore, is to try to sort out those solutions which have reflective properties with respect to the structural character of reality from those which do not have such properties. The thesis addresses this task by introducing the idea of hermeneutical field theory. In this theory the notion of a semiotic operator or semiotic quantum plays a central role. More specifically, this quantum is considered to be the carrier of hermeneutical force. It arises as a field property at the complex, horizontal membrane-manifold linking human consciousness with different levels of scale of reality. When taken collectively, the aforementioned set of equations gives expression to the structural character of hermeneutical field theory. Therefore, when one begins to run concrete variables through the theory underlying these equations, one encounters various kinds of hermeneutical constraints and degrees of freedom. These constraints and degrees of freedom characterize the dialectical engagement of consciousness and reality as one seeks to acquire understanding concerning the above mentioned variables and the context which gives rise to them. Hermeneutical field theory is really the study of the factors that affect the state of the six internal
Post-measurement bipartite entanglement entropy in conformal field theories
NASA Astrophysics Data System (ADS)
Rajabpour, M. A.
2015-08-01
We derive exact formulas for bipartite von Neumann entanglement entropy after partial projective local measurement in (1 +1 ) -dimensional conformal field theories with periodic and open boundary conditions. After defining the setup we will check numerically the validity of our results in the case of Klein-Gordon field theory (coupled harmonic oscillators) and spin-1 /2 X X chain in a magnetic field. The agreement between analytical results and the numerical calculations is very good. We also find a lower bound for localizable entanglement in coupled harmonic oscillators.
Cold atom simulation of interacting relativistic quantum field theories.
Cirac, J Ignacio; Maraner, Paolo; Pachos, Jiannis K
2010-11-01
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations. PMID:21231152
Dualities among one-time field theories with spin, emerging from a unifying two-time field theory
Bars, Itzhak; Quelin, Guillaume
2008-06-15
The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS{sub d-k}xS{sup k}, and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
Dualities among one-time field theories with spin, emerging from a unifying two-time field theory
NASA Astrophysics Data System (ADS)
Bars, Itzhak; Quélin, Guillaume
2008-06-01
The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdSd-k×Sk, and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
Prime Numbers, Quantum Field Theory and the Goldbach Conjecture
NASA Astrophysics Data System (ADS)
Sanchis-Lozano, Miguel-Angel; Barbero G., J. Fernando; Navarro-Salas, José
2012-09-01
Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators bp\\dag — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
Generalized conservation laws in non-local field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Quantum field theory constrains traversable wormhole geometries
Ford, L.H. |; Roman, T.A. |
1996-05-01
Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
Warped conformal field theory as lower spin gravity
NASA Astrophysics Data System (ADS)
Hofman, Diego M.; Rollier, Blaise
2015-08-01
Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.
A gauge field theory of fermionic continuous-spin particles
NASA Astrophysics Data System (ADS)
Bekaert, X.; Najafizadeh, M.; Setare, M. R.
2016-09-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Conformal field theory out of equilibrium: a review
NASA Astrophysics Data System (ADS)
Bernard, Denis; Doyon, Benjamin
2016-06-01
We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.
Thermofield dynamics extension of the open string field theory
NASA Astrophysics Data System (ADS)
Botta Cantcheff, M.; Scherer Santos, R. J.
2016-03-01
We study the application of the rules of thermofield dynamics (TFD) to the covariant formulation of open-string field theory. We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended Becchi, Rouet, Stora and Tyutin (BRST) charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement, and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it of which the results at tree level agree with those of the conventional theory.
Effective Field Theories from Soft Limits of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
Consistent constraints on the Standard Model Effective Field Theory
NASA Astrophysics Data System (ADS)
Berthier, Laure; Trott, Michael
2016-02-01
We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S, T analysis is modified by the theory errors we include as an illustrative example.
Quantum field theories on algebraic curves. I. Additive bosons
NASA Astrophysics Data System (ADS)
Takhtajan, Leon A.
2013-04-01
Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.
Thermodynamics of perfect fluids from scalar field theory
NASA Astrophysics Data System (ADS)
Ballesteros, Guillermo; Comelli, Denis; Pilo, Luigi
2016-07-01
The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of Stückelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the thermodynamic variables, we find that a complete thermodynamic picture requires the four Stückelberg fields. We show that thermodynamic stability plus the null-energy condition imply dynamical stability. We also argue that a consistent thermodynamic interpretation is not possible if any of the shift symmetries is explicitly broken.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Regularization methods for Nuclear Lattice Effective Field Theory
NASA Astrophysics Data System (ADS)
Klein, Nico; Lee, Dean; Liu, Weitao; Meißner, Ulf-G.
2015-07-01
We investigate Nuclear Lattice Effective Field Theory for the two-body system for several lattice spacings at lowest order in the pionless as well as in the pionful theory. We discuss issues of regularizations and predictions for the effective range expansion. In the pionless case, a simple Gaussian smearing allows to demonstrate lattice spacing independence over a wide range of lattice spacings. We show that regularization methods known from the continuum formulation are necessary as well as feasible for the pionful approach.
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Chiral Effective Field Theory in the $\\Delta$-resonance region
Vladimir Pascalutsa
2006-09-18
I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the $\\Delta(1232)$, the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the $\\Delta$-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Inductive approach towards a phenomenologically more satisfactory unififed field theory
Rayski, J.; Rayski J.M. Jnr.
1985-11-01
A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.
Negative-frequency modes in quantum field theory
NASA Astrophysics Data System (ADS)
Dickinson, Robert; Forshaw, Jeff; Millington, Peter
2015-07-01
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.
A Variational Statistical-Field Theory for Polar Liquid Mixtures
NASA Astrophysics Data System (ADS)
Zhuang, Bilin; Wang, Zhen-Gang
Using a variational field-theoretic approach, we derive a molecularly-based theory for polar liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy of mixing and the dielectric constant as functions of mixture composition. Using only the dielectric constants and the molar volumes of the pure liquid constituents, the theory evaluates the mixture dielectric constants in good agreement with the experimental values for a wide range of liquid mixtures, without using adjustable parameters. In addition, the theory predicts that liquids with similar dielectric constants and molar volumes dissolve well in each other, while sufficient disparity in these parameters result in phase separation. The calculated miscibility map on the dielectric constant-molar volume axes agrees well with known experimental observations for a large number of liquid pairs. Thus the theory provides a quantification for the well-known empirical ``like-dissolves-like'' rule. Bz acknowledges the A-STAR fellowship for the financial support.
Motion of small bodies in classical field theory
Gralla, Samuel E.
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles. PMID:24702348
Noncausal propagation in spin-0 theories with external field interactions
NASA Technical Reports Server (NTRS)
Guertin, R. F.; Wilson, T. L.
1977-01-01
The two-component Sakata-Taketani (ST) spin-0 theory and the single-component Klein-Gordon theory are obtained from the five-component Duffin-Kemmer-Petiau (DKP) theory with six types of external field interactions by means of a Peirce decomposition. Whereas the DKP equation manifests the covariance, the ST equation manifests the causal properties. In particular, the presence of noncausal wave propagation when there is coupling to a second-rank tensor field is apparent from the form of the ST equation, in which the coefficients of all the space derivatives depend on the external field. The results indicate that the causal properties of higher-spin equations should also be obvious when they are expressed in 2(2J + 1)-component Schroedinger form
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
NASA Astrophysics Data System (ADS)
Schenkel, Alexander
2012-10-01
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that these theories have an improved behaviour at short distances, i.e. in the ultraviolet. In part three we study homomorphisms between and connections on noncommutative vector bundles. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of bimodules is clarified. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.
BPS index and 4d N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Sakai, Kazuhiro
2016-07-01
We study the BPS index for the four-dimensional rank-one N = 2 superconformal field theories H 0 , H 1 , H 2 , E 6 , E 7 , E 8. We consider compactifications of the E-string theory on T 2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.
The Solar hep Process in Effective Field Theory
T.-S. Park; L. E. Marcucci; R. Schiavilla; M. Viviani; A. Kievsky; S. Rosati; K. Kubodera; D.-P. Min; M. Rho
2001-09-01
Using effective field theory, we calculate the S-factor for the hep process in a totally parameter-free formulation. The transition operators are organized according to chiral counting, and their matrix elements are evaluated using the realistic nuclear wave functions obtained in the Correlated-hyperspherical-harmonics method. Terms of up to next-to-next-to-next-to-leading order in heavy-baryon chiral perturbation theory are considered. Fixing the only parameter in the theory by fitting the tritium beta-decay rate, we predict the hep S-factor with accuracy better than {approx} 20%.
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
Ydri, Badis
2010-10-31
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar {phi}{sup 4} field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at {theta} = 0 there must exist a novel fixed point at {theta} = {infinity} corresponding to the quartic hermitian matrix model.
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
NASA Astrophysics Data System (ADS)
Ydri, Badis
2010-10-01
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar φ4 field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at θ = 0 there must exist a novel fixed point at θ = ∞ corresponding to the quartic hermitian matrix model.
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories. PMID:27494465
Modular Hamiltonian for Excited States in Conformal Field Theory
NASA Astrophysics Data System (ADS)
Lashkari, Nima
2016-07-01
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Zn replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Closed string cohomology in open string field theory
NASA Astrophysics Data System (ADS)
Moeller, Nicolas; Sachs, Ivo
2011-07-01
We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten's 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.
Contour-ordered Green's functions in stochastic field theory
NASA Astrophysics Data System (ADS)
Honkonen, J.
2013-06-01
We briefly review the functional formulation of the perturbation theory for various Green's functions in quantum field theory. In particular, we discuss the contour-ordered representation of Green's functions at a finite temperature. We show that the perturbation expansion of time-dependent Green's functions at a finite temperature can be constructed using the standard Wick rules in the functional form without introducing complex time and evolution backward in time. We discuss the factorization problem for the corresponding functional integral. We construct the Green's functions of the solution of stochastic differential equations in the Schwinger-Keldysh form with a functional-integral representation with explicitly intertwined physical and auxiliary fields.
Negative contributions to S in an effective field theory
Dobrescu, Bogdan A.; Terning, John
1997-09-19
We show that an effective field theory that includes non-standard couplings between the electroweak gauge bosons and the top and bottom quarks may yield negative contributions to both the S and T oblique radiative electroweak parameters. We find that such an effective field theory provides a better fit to data than the standard model (the {chi}{sup 2} per degree of freedom is half as large). We examine in some detail an illustrative model where the exchange of heavy scalars produces the correct type of non-standard couplings.
Approaches to the sign problem in lattice field theory
NASA Astrophysics Data System (ADS)
Gattringer, Christof; Langfeld, Kurt
2016-08-01
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focusing on two more recent methods: dualization to worldline type of representations and the density-of-states approach.
A field theory of piezoelectric media containing dislocations
Taupin, V. Fressengeas, C.; Ventura, P.; Lebyodkin, M.
2014-04-14
A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.
A field theory approach to the dynamics of classical particles
NASA Astrophysics Data System (ADS)
McCowan, David; Mazenko, Gene
2012-02-01
For nearly 30 years, mode-coupling theory (MCT) has been regarded as the de facto theoretic description of dense fluids and the transition from the fluid to glassy state. But MCT is limited by its ad hoc construction and lacks a mechanism to institute corrections. We present a new fundamental theory for the kinetics of systems of classical particles which represents a unification of kinetic theory, Brownian motion and field theory. It is developed from first principles via a self-consistent perturbation in terms of an effective two-body potential, and we use this theory to investigate the existence of ergodic-nonergodic (ENE) transitions near the liquid-glass transition. After a brief introduction of the theory, we will address the development of a kinetic equation of the memory function form. The memory function kernel (or self-energy) determined by the theory shares properties with the MCT form, however our theory provides the crucial advantage of well-defined, perturbative corrections.
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Dualities between semiclassical strings and quantum gauge field theories
NASA Astrophysics Data System (ADS)
Ouyang, Peter
In this thesis we study several examples of the correspondence between gauge field theories and string theories. A recurrent theme of these studies is that distinctively quantum mechanical behavior on the gauge theory side of the correspondence can have a classical or semiclassical description in terms of string calculations, as one might expect from general considerations of open/closed duality. We begin in Chapter 1 by reviewing the simplest duality, which relates Type IIB supergravity in AdS5 x S5 to N = 4 SU(N) gauge theory at large N. Working with this background spacetirne, we turn to a study of D-brane probes with large quantum numbers in Chapter 2. We employ semiclassical methods to compute the excitation spectrum of these D-branes, including corrections of order 1/N, which are related to loop effects in the dual field theory. In Chapter 3 we discuss the gauge/gravity duals with N = 1 supersymmetry which arise from placing D-branes at a conifold singularity. The inclusion of fractional D3-branes breaks conformal invariance, leading to a rich variety of phenomena in the gauge theory, among them chiral anomalies, a cascade of Seiberg dualities and confinement in the infrared. We pay particular attention to the chiral anomalies of the gauge theory and show that they can be described in terms of classical spontaneous symmetry breaking in the dual string theory. In accord with low-energy confinement in the field theory, almost all of the moduli of the supergravity solution are fixed; we conclude Chapter 3 with some observations on the possibility of stabilizing the volume of the compact space in which the conifold is embedded. Finally, in Chapter 4 we study versions of the conifold theory with D7-branes, which introduce fundamental matter into the gauge theory. By solving the classical supergravity equations of motion we identify a variant of the Klebanov-Strassler duality cascade where the rate of the cascade decreases as the theory flows to low energies.
Velocity-Field Theory, Boltzmann's Transport Equation and Geometry
NASA Astrophysics Data System (ADS)
Ichinose, Shoichi
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
NASA Astrophysics Data System (ADS)
Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, René; Park, Jeong-Hyuck
2015-12-01
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations.
Positive Energy Conditions in 4D Conformal Field Theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus; Prilepina, Valentina
2016-03-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality avgT00 >= - C /L4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the ``conformal collider'' constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
The Effective Field Theory Approach to Fluid Dynamics
NASA Astrophysics Data System (ADS)
Endlich, Solomon George Shamsuddin Osman
In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
On gradient field theories: gradient magnetostatics and gradient elasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2014-09-01
In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot-Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach-Koehler stress equation, Peach-Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Field-Based Concerns about Fourth-Generation Evaluation Theory.
ERIC Educational Resources Information Center
Lai, Morris K.
Some aspects of fourth generation evaluation procedures that have been advocated by E. G. Guba and Y. S. Lincoln were examined empirically, with emphasis on areas where there have been discrepancies between theory and field-based experience. In fourth generation evaluation, the product of an evaluation is not a set of conclusions, recommendations,…
Sketch of J. R. Kantor's Psychological Interbehavioral Field Theory
ERIC Educational Resources Information Center
Delprato, Dennis J.; Smith, Noel W.
2009-01-01
We provide a sketch of J. R. Kantor's (1959, 1971) psychological interbehavioral field (IBF) theory by identifying 9 essential points and briefly discussing each. The main emphasis of this sketch is on the foundation of Kantor's thinking, the IBF. Suggestions for further study are provided.
The effective field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg00(u))n at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
Approximate Near-Field Blast Theory: A Generalized Approach
Hutchens, G.J.
1999-10-25
A method for analyzing strong shock waves in arbitrary one-dimensional geometry is presented. An approximation to classical Taylor-Sedov theory is extended to the near-field case where source mass is not negligible, accounting for differences in the chemical properties of the source mass and ambient medium. Results from example calculations are compared with previously published analytical formulae.
Schr"odinger's Unified Field Theory: Physics by Public Relations
NASA Astrophysics Data System (ADS)
Halpern, Paul
2009-05-01
We will explore the circumstances surrounding Erwin Schr"odinger's announcement in January 1947 that he had developed a comprehensive unified field theory of gravitation and electromagnetism. We will speculate on Schr"odinger's motivations for the mode and tone of his statements, consider the reaction of the international press within the context of the postwar era, and examine Einstein's response.
Holography and hydrodynamics for EMD theory with two Maxwell fields
NASA Astrophysics Data System (ADS)
Smolic, Milena
2013-03-01
We use `generalized dimensional reduction' to relate a specific Einstein-Max-well-Dilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higher-dimensional AdS gravity (with no higher-dimensional Maxwell field). In general, this is a dimensional reduction over compact Einstein spaces in which the dimension of the compact space is continued to non-integral values. Specifically, we perform a non-diagonal Kaluza-Klein (KK) reduction over a torus, involving two KK gauge fields. Our aim is to determine the holographic dictionary and hydrodynamic behaviour of the lower-dimensional theory by performing the generalized dimensional reduction on AdS. We study a specific example of a black brane carrying a wave, whose universal sector is described by gravity coupled to two Maxwell fields, three neutral scalars and an axion, and compute the first order transport coefficients of the dual theory. In these theories {{widehat{ζ}}_s}/widehat{η}<2( {1/( {d-1} )-widehat{c}_s^2} ) , where {{widehat{c}}_s} is the speed of sound, violating a conjectured bound, but an alternative bound is satisfied.
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Chiral field theories as models for hadron substructure
Kahana, S.H.
1987-03-01
A model for the nucleon as soliton of quarks interacting with classical meson fields is described. The theory, based on the linear sigma model, is renormalizable and capable of including sea quarks straightforwardly. Application to nuclear matter is made in a Wigner-Seitz approximation.
Probing {N}=2 superconformal field theories with localization
NASA Astrophysics Data System (ADS)
Fiol, Bartomeu; Garolera, Blai; Torrentsa, Genís
2016-01-01
We use supersymmetric localization to study probes of four dimensional Lagrangian {N}=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of {N}=4 supersymmetric Yang-Mills theory.
Field theory as a tool to constrain new physics models
NASA Astrophysics Data System (ADS)
Maas, Axel
2015-08-01
One of the major problems in developing new physics scenarios is that very often the parameters can be adjusted such that in perturbation theory almost all experimental low-energy results can be accommodated. It is therefore desirable to have additional constraints. Field-theoretical considerations can provide such additional constraints on the low-lying spectrum and multiplicities of models. Especially for theories with elementary or composite Higgs particle the Fröhlich-Morchio-Strocchi (FMS) mechanism provides a route to create additional conditions, though showing it to be at work requires genuine non-perturbative calculations. The qualitative features of this procedure are discussed for generic 2-Higgs-doublet models (2HDMs), grand-unified theories (GUTs) and technicolor-type theories.
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
ERIC Educational Resources Information Center
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of…
Decoherence in an interacting quantum field theory: The vacuum case
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2010-03-15
We apply the decoherence formalism to an interacting scalar field theory. In the spirit of the decoherence literature, we consider a 'system field' and an 'environment field' that interact via a cubic coupling. We solve for the propagator of the system field, where we include the self-energy corrections due to the interaction with the environment field. In this paper, we consider an environment in the vacuum state (T=0). We show that neglecting inaccessible non-Gaussian correlators increases the entropy of the system as perceived by the observer. Moreover, we consider the effect of a changing mass of the system field in the adiabatic regime, and we find that at late times no additional entropy has been generated.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Gauge fields in graphene with nonuniform elastic deformations: A quantum field theory approach
NASA Astrophysics Data System (ADS)
Arias, Enrique; Hernández, Alexis R.; Lewenkopf, Caio
2015-12-01
We investigate the low-energy continuum limit theory for electrons in a graphene sheet under strain. We use the quantum field theory in curved spaces to analyze the effect of the system deformations into an effective gauge field. We study both in-plane and out-of-plane deformations and obtain a closed expression for the effective gauge field due to arbitrary nonuniform sheet deformations. The obtained results reveal a remarkable relation between the local-pseudomagnetic field and the Riemann curvature, so far overlooked.
G{sub Ep}/G{sub Mp} ratio by polarization transfer in ep {yields} ep
Mark K. Jones; Konrad A. Aniol; F.T. Baker; J. Berthot; Pierre Bertin; William Bertozzi; A. Besson; Louis Bimbot; Werner Boeglin; Ed Brash; D. Brown; John Calarco, Larry S. Cardman; C.-C. Chang; Jian-ping Chen; Eugene Chudakov; Steve Churchwell; Evaristo Cisbani; Dan Dale; R. De Leo; Alexandre Deur; Brian Diederich; John Domingo; Martin B. Epstein; Lars Ewell; Kevin Fissum; A. Fleck; Helene Fonvieille; Salvatore Frullani; J. Gao; Franco Garibaldi; Ashot Gasparian; G. Gerstner; Shalev Gilad; Ron Gilman.; Alexander Glamazdin; Charles Glashausser; Javier Gomez; V. Gorbenko; A. Green; Jens-Ole Hansen; Howell, C.R.; Huber, G.M.; Mauro Iodice; Kees de Jager; Stephanie Jaminion; Xiangdong Jiang; William Kahl; James J. Kelly; M. Khayat; Laird H. Kramer; G. Kumbartzki; Michael Kuss; E. Lakuriki; G. Lavessiere; John J. LeRose; Meme Liang; Richard Lindgren; Nilanga Liyanage; George Lolos; R. Macri; Richard Madey; Sergey Malov; Dimitri Margaziotis; Pete Markowitz; Kathy McCormick; Justin McIntyre; R.L. van der Meer; R. Michaels; B.D. Milbrath; Jean Mougey; S.K. Nanda; E.A.J.M. Offerman; Z. Papandreou; Charles F. Perdrisat; Gerassimos G. Petratos; N.M. Piskunov; R.I. Pomatsalyuk; David Prout; Vina Punjabi; Gilles Quemener; Ronald Ransome; Brian Raue; Yves Roblin; Rikki Roche; Gary Rutledge; Paul Rutt; Arun Saha; Teijiro Saito; Adam Sarty; Timothy Smith; P. Sorokin; Steffen Strauch; R. Suleiman; K. Takahashi; Jeff Templon; Luminita Todor; Paul E. Ulmer; Guido M. Urciuoli; Pascal Vernin; B. Vlahovic; H. Voskanyan, H.; Krishni Wijesooriya; Bogdan Wojtsekhowski; R.J. Woo; F. Xiong; George Dan Zainea; Z.-L. Zhou
2000-02-14
The ratio of the proton's elastic electromagnetic form factors, G{sub Ep}/G{sub Mp} was obtained by measuring P{sub t} and P{ell}, the transverse and the longitudinal recoil proton polarization, respectively. For elastic ep {yields} ep, G{sub Ep}/G{sub Mp} is proportional to P{sub t}/P{ell}. Simultaneous measurement of P{sub t} and P{ell} in a polarimeter provides good control of the systematic uncertainty. The results for the ratio G{sub Ep}/G{sub Mp} show a systematic decrease as Q{sup 2} increases from 0.5 to 3.5 GeV{sup 2}, indicating for the first time a definite difference in the spatial distribution of charge and magnetization currents in the proton.
New symbolic tools for differential geometry, gravitation, and field theory
NASA Astrophysics Data System (ADS)
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
Inflationary solutions in the nonminimally coupled scalar field theory
NASA Astrophysics Data System (ADS)
Koh, Seoktae; Kim, Sang Pyo; Song, Doo Jong
2005-08-01
We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous spacetimes and the long-wavelength approximation is employed to find the homogeneous solutions during an inflation period. The constraints that lead to a sufficient number of e-folds, a necessary condition for inflation, are found for the nonminimal coupling constant and initial conditions of the scalar field for inflation potentials. In particular, we numerically find an inflationary solution in the new inflation model of a nonminimal scalar field.
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-15
The ''basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a {phi}{sup 4} interaction to three-loop order. (c) 2000 The American Physical Society.
Reconstructing inflationary paradigm within Effective Field Theory framework
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan
2016-03-01
In this paper my prime objective is to analyse the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from recent Planck 2015 and Planck 2015 + BICEP2/Keck Array data. By explicit computation I have reconstructed the structural form of the inflationary potential by constraining the Taylor expansion co-efficients appearing in the generic expansion of the potential within the Effective Field Theory. Next I have explicitly derived, a set of higher order inflationary consistency relationships, which would help us to break the degeneracy between various class of inflationary models by differentiating them. I also provided two simple examples of Effective Theory of inflation- inflection-point model and saddle-point model to check the compatibility of the prescribed methodology in the light of Planck 2015 and Planck 2015 + BICEP2/Keck Array data. Finally, I have also checked the validity of the prescription by estimating the cosmological parameters and fitting the theoretical CMB TT, TE and EE angular power spectra with the observed data within the multipole range 2 < l < 2500.
M Theory on AdSp x 511-p and superconformal field theories
Aharony, Ofer; Yaron, Oz; Zheng, Yin
1998-04-01
We study the large N limit of the interacting superconformal field theories associated with N M5 branes or M2 branes using the recently proposed relation between these theories and M theory on AdS spaces. We first analyze the spectrum of chiral operators of the 6d (0, 2) theory associated with M5 branes in flat space, and find full agreement with earlier results obtained using its DLCQ description as quantum mechanics on a moduli space of instantons. We then perform a similar analysis for the D{sub N} type 6d (0, 2) theories associated with M5 branes at an R{sup 5}/Z{sub 2} singularity, and for the 3d N = 8 superconformal field theories associated with M2 branes in flat space and at an R{sup 8}/Z{sub 2} singularity respectively. Little is known about these three theories, and our study yields for the first time their spectrum of chiral operators (in the large N limit).
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S.
2013-03-25
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
Entanglement of low-energy excitations in conformal field theory.
Alcaraz, Francisco Castilho; Ibáñez Berganza, Miguel; Sierra, Germán
2011-05-20
In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Rényi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Rényi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT. PMID:21668218
Entanglement of Low-Energy Excitations in Conformal Field Theory
Alcaraz, Francisco Castilho; Ibanez Berganza, Miguel; Sierra, German
2011-05-20
In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.
The unitary conformal field theory behind 2D Asymptotic Safety
NASA Astrophysics Data System (ADS)
Nink, Andreas; Reuter, Martin
2016-02-01
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d > 2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c = 25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d > 2 dimensions and Polyakov's induced gravity action in two dimensions.
The Effective Field Theory of Dark Matter and Structure Formation
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P
2014-06-01
We develop the effective field theory of cosmological large scale structure. We start from the collisionless Boltzmann equation and integrate out short modes of a dark matter/dark energy dominated universe (LambdaCDM) whose matter is comprised of massive particles as used in cosmological simulations. This establishes a long distance effective fluid, valid for length scales larger than the non-linear scale ~ 10 Mpc, and provides the complete description of large scale structure formation. Extracting the time dependence, we derive recursion relations that encode the perturbative solution. This is exact for the matter dominated era and quite accurate in LambdaCDM also. The effective fluid is characterized by physical parameters, including sound speed and viscosity. These two fluid parameters play a degenerate role with each other and lead to a relative correction from standard perturbation theory of the form ~ 10^{-6}c^2k^2/H^2. Starting from the linear theory, we calculate corrections to cosmological observables, such as the baryon-acoustic-oscillation peak, which we compute semi-analytically at one-loop order. Due to the non-zero fluid parameters, the predictions of the effective field theory agree with observation much more accurately than standard perturbation theory and we explain why. We also discuss corrections from treating dark matter as interacting or wave-like and other issues.
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
Gravitation: Field theory par excellence Newton, Einstein, and beyond
Yilmaz, H.
1984-09-01
Newtonian gravity satifies the two principles of equivalence m/sub i/ = m/sub p/ (the passive principle) and m/sub a/ = m/sub p/ (the active principle). A relativistic gauge field concept in D = s+1 dimensional curved-space will, in general, violate these two principles as in m/sub p/ = ..cap alpha..m/sub i/, m/sub a/ = lambdam/sub p/ where ..cap alpha.. = D: 3 and lambda measures the presence of the field stress-energy t/sup ..nu..//sub ..mu../ in the field equations. It is shown that ..cap alpha.. = 1, lambda = 0 corresponds to general relativity and ..cap alpha.. = 1, lambda = 1 to the theory of the author. It is noted that the correspondence limit of general relativity is not Newton's theory but a theory suggested by Robert Hooke a few years before Newton published his in Principia. The gauge is independent of the two principles but had to do with local special relativistic correspondence and compatibility with quantum mechanics. It is shown that unless ..cap alpha.. = 1, lambda = 1 the generalized theory cannot predict correctly many observables effects, including the 532'' per century Newtonian part in Mercury's perihelion advance.
Power counting and Wilsonian renormalization in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
2006-03-01
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the "scale-space." We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Axiomatics of Galileo-invariant quantum field theory
Dadashev, L.A.
1986-03-01
The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms.
Double metric, generalized metric, and α' -deformed double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2016-03-01
We relate the unconstrained "double metric" of the "α' -geometry" formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b -field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application, we prove that, to first order in α' and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in α' the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.
Irreversibility and higher-spin conformal field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2000-08-01
I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.
Heavy dark matter annihilation from effective field theory.
Ovanesyan, Grigory; Slatyer, Tracy R; Stewart, Iain W
2015-05-29
We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments. PMID:26066425
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; Schiavilla, Rocco; Viviani, Michele
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power countingmore » is constructed.« less
Large N correlation functions in superconformal field theories
NASA Astrophysics Data System (ADS)
Rodriguez-Gomez, Diego; Russo, Jorge G.
2016-06-01
We compute correlation functions of chiral primary operators in mathcal{N}=2 super-conformal theories at large N using a construction based on supersymmetric localization recently developed by Gerchkovitz et al. We focus on mathcal{N}=4 SYM as well as on supercon-formal QCD. In the case of mathcal{N}=4 we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large N limit. The final correlators admit a simple generalization to a finite N formula which exactly matches the various small N results in the literature.
Advanced mean-field theory of the restricted Boltzmann machine
NASA Astrophysics Data System (ADS)
Huang, Haiping; Toyoizumi, Taro
2015-05-01
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.
Stationary axisymmetric fields in a teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Saez, D.
1984-12-01
The stationary axisymmetric field in the tetrad theory of gravitation of Moller (1978) and hence (as shown by Meyre, 1982) in the teleparallel limit of the gauge theory of Hehl et al. (1978) is investigated analytically. A set of tetrads satisfying the Moller equations and giving a Kerr metric is defined, and its existence is proved. It is suggested that the introduction of suitable conditions could reduce the number of tetrads in the Kerr case to one or a small number, and that the present analytical techniques could be applied to other stationary axisymmetric metrics of general relativity.
Motion of small bodies in classical field theory
NASA Astrophysics Data System (ADS)
Gralla, Samuel E.
2010-04-01
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Enhanced gauge symmetry and winding modes in double field theory
NASA Astrophysics Data System (ADS)
Aldazabal, G.; Graña, M.; Iguri, S.; Mayo, M.; Nuñez, C.; Rosabal, J. A.
2016-03-01
We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1) × U(1) symmetry to SU(2) × SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with Oleft(d+3,d+3right)/Oleft(d+3right)× Oleft(d+3right) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.
Einstein-aether theory with a Maxwell field: General formalism
Balakin, Alexander B.; Lemos, José P.S.
2014-11-15
We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.
Lally, Michelle; Zimet, Gregory; Kahn, Jessica A.
2015-01-01
Abstract Prior to issuing formal HIV pre-exposure prophylaxis (PrEP) clinical practice guidelines in 2014, the US Centers for Disease Control and Prevention (CDC) had released interim guidance for oral PrEP use among adults. Because oral PrEP may be used off-label for youth and may soon be indicated for minor adolescents, we examined the potential adoption of the interim guidance among clinicians who care for HIV-infected and at-risk youth. Individual, semi-structured interviews were conducted with 15 US clinicians who were recruited through an adolescent HIV research network. The theory-driven interview guide, consisting primarily of open-ended questions, assessed demographics, familiarity with the guidance, attitudes toward the guidance, and attitudes toward the use of the guidance for adult and adolescent patients. Transcripts were analyzed using framework analysis. Most clinicians (11/15) reported that the guidance was compatible with their practice, although several reported that some aspects, particularly frequency of follow-up visits, needed to be tailored to meet their patients' needs. We found variability in clinician reported characteristics of appropriate PrEP candidates (e.g., youth with substance use and mental health issues were noted to be both suitable and unsuitable PrEP candidates) and PrEP use in serodiscordant couples (e.g., whether PrEP would be recommended to a patient whose HIV-infected partner is virally suppressed). Clinician reported steps for initiation, monitoring, and discontinuing PrEP were largely consistent with the guidance. The observed variability in clinician practice with regard to oral PrEP may be reduced through interventions to educate clinicians about the content and rationale for guideline recommendations. PMID:25692683
Scale-free phase field theory of dislocations.
Groma, István; Vandrus, Zoltán; Ispánovity, Péter Dusán
2015-01-01
According to recent experimental and numerical investigations, if a characteristic length (such as grain size) of a specimen is in the submicron size regime, several new interesting phenomena emerge during the deformation. Since in such systems boundaries play a crucial role, to model the plastic response it is crucial to determine the dislocation distribution near the boundaries. In this Letter, a phase-field-type continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near internal boundaries, is presented. Since the dislocation-dislocation interaction is scale free (1/r), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations. PMID:25615479
Scale-Free Phase Field Theory of Dislocations
NASA Astrophysics Data System (ADS)
Groma, István; Vandrus, Zoltán; Ispánovity, Péter Dusán
2015-01-01
According to recent experimental and numerical investigations, if a characteristic length (such as grain size) of a specimen is in the submicron size regime, several new interesting phenomena emerge during the deformation. Since in such systems boundaries play a crucial role, to model the plastic response it is crucial to determine the dislocation distribution near the boundaries. In this Letter, a phase-field-type continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near internal boundaries, is presented. Since the dislocation-dislocation interaction is scale free (1 /r ), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations.
Canonical non-Abelian dual transformations in supersymmetric field theories
Curtright, T.; Zachos, C.
1995-07-15
A generating functional {ital F} is found for a canonical non-Abelian dual transformation which maps the supersymmetric chiral O(4) {sigma} model to an equivalent supersymmetric extension of the dual {sigma} model. This {ital F} produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {ital symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional {ital T} which relates wave functions in the two quantum theories is argued to be {ital exactly} given by {ital T}=exp({ital iF}).
Discrete field theories and spatial properties of strings
Klebanov, I.; Susskind, L.
1988-10-01
We use the ground-state wave function in the light-cone gauge to study the spatial properties of fundamental strings. We find that, as the cut-off in the parameter space is removed, the strings are smooth and have a divergent size. Guided by these properties, we consider a large-N lattice gauge theory which has an unstable phase where the size of strings diverges. We show that this phase exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero for this equivalence to hold. Thus, exact rotation and translation invariance is restored in a discrete space. This suggests that the number of fundamental short-distance degrees of freedom in string theory is much smaller than in a conventional field theory. 11 refs., 4 figs.
The spectral theory of a functional-difference operator in conformal field theory
NASA Astrophysics Data System (ADS)
Takhtajan, L. A.; Faddeev, L. D.
2015-04-01
We consider the functional-difference operator H=U+U-1+V, where U and V are the Weyl self-adjoint operators satisfying the relation UV=q2VU, q=eπ iτ, τ>0. The operator H has applications in the conformal field theory and representation theory of quantum groups. Using the modular quantum dilogarithm (a q-deformation of the Euler dilogarithm), we define the scattering solution and Jost solutions, derive an explicit formula for the resolvent of the self-adjoint operator H on the Hilbert space L2( R), and prove the eigenfunction expansion theorem. This theorem is a q-deformation of the well-known Kontorovich-Lebedev transform in the theory of special functions. We also present a formulation of the scattering theory for H.
From effective field theories to effective density functionals in and beyond the mean field
NASA Astrophysics Data System (ADS)
Grasso, M.; Lacroix, D.; van Kolck, U.
2016-06-01
Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy–density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.
Mean-field theory of echo state networks
NASA Astrophysics Data System (ADS)
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
Mean-field theory of echo state networks.
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study "echo state networks," networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion. PMID:23679475
The adhesion model as a field theory for cosmological clustering
Rigopoulos, Gerasimos
2015-01-01
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.
A condensed matter field theory for quantum plasmonics
NASA Astrophysics Data System (ADS)
Ballout, Fouad; Hess, Ortwin
In recent years plasmonics has advanced to ever decreasing length scales reaching dimensions comparable to the de broglie wavelength of an electron, which has a manifest influence on the plasmon dispersion relation. The associated phenomenology lies beyond the reach of the classical drude free electron theory or its nonlocal extension and adequate models are needed to address the quantum matter aspects of light-matter interaction that are responsible for plasmonicquantum size effects. We present on the basis of the jellium model a quantum field theory of surface-plasmon polaritons in which they emerge as extended objects as a result of an inhomogeneous condensation of bosons around a topological singularity describing the surface. The benefit of this approach lies in relating the electromagnetic fields belonging to such a macroscopic quantum state with the surface topology and nonlocal responsefunction (expressed in terms of the retarded photon self-energy) of the delimited electron gas sustaining that state.
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.
Cluster-like coordinates in supersymmetric quantum field theory
Neitzke, Andrew
2014-01-01
Recently it has become apparent that N=2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1–211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore. PMID:24982190
Shape dependence of entanglement entropy in conformal field theories
NASA Astrophysics Data System (ADS)
Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
2016-04-01
We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R^{1,d-1} . We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ /C_T=π^2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.
Effective field theory of quantum gravity coupled to scalar electrodynamics
NASA Astrophysics Data System (ADS)
Ibiapina Bevilaqua, L.; Lehum, A. C.; da Silva, A. J.
2016-05-01
In this work, we use the framework of effective field theory to couple Einstein’s gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where quantum mechanics and general relativity are perfectly compatible. We consider the effective field theory up to dimension six operators, corresponding to processes involving one-graviton exchange. Studying the renormalization group functions, we see that the beta function of the electric charge is positive and possesses no contribution coming from gravitational interaction. Our result indicates that gravitational corrections do not alter the running behavior of the gauge coupling constants, even if massive particles are present.
A hydrodynamic approach to non-equilibrium conformal field theories
NASA Astrophysics Data System (ADS)
Bernard, Denis; Doyon, Benjamin
2016-03-01
We develop a hydrodynamic approach to non-equilibrium conformal field theory. We study non-equilibrium steady states in the context of one-dimensional conformal field theory perturbed by the T\\bar{T} irrelevant operator. By direct quantum computation, we show, to first order in the coupling, that a relativistic hydrodynamic emerges, which is a simple modification of one-dimensional conformal fluids. We show that it describes the steady state and its approach, and we provide the main characteristics of the steady state, which lies between two shock waves. The velocities of these shocks are modified by the perturbation and equal the sound velocities of the asymptotic baths. Pushing this approach further, we are led to conjecture that the approach to the steady state is generically controlled by the power law t -1/2, and that the widths of the shocks increase with time according to t 1/3.
Development of mean-field electrical double layer theory
NASA Astrophysics Data System (ADS)
Yike, Huang; Xiaohong, Liu; Shu, Li; Tianying, Yan
2016-01-01
In order to understand the electric interfacial behavior, mean field based electric double layer (EDL) theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice-gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversion among them can be achieved by reducing the basic assumptions. Project supported by the National Natural Science Foundation of China (Grant Nos. 21421001, 21373118, and 21203100), the Natural Science Foundation of Tianjin, China (Grant No. 13JCQNJC06700), the MOE Innovation Team of China (Grant No. IRT13022), and NFFTBS (Grant No. J1103306).
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standardmore » operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.« less
Anomaly cancelation in field theory and F-theory on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas
2016-05-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
Baker, W.M.
1980-01-01
We examine the scale-invariant Lagrangian densities in Riemannian and non-Riemannian spacetimes. We find that the most general scale-invariant Lagrangian density of a Riemann-Cartan spacetime can also be reduced in a manner similar to that demonstrated earlier by Lanczos for the Riemannian case. However, this type of reduction process is not possible in a non-metric spacetime. Duality transformations of the type defined in electromagnetic theory are discussed and classified in terms of those transformations having a direct relationship to an internal symmetry structure of a given gauge theory and those that do not. We show that to build a satisfactory generalized electromagnetic type theory with local duality invariance into a gauge theory, as at least a part of its internal symmetry structure, requires a group no smaller than SO/sub 3/ or (SU/sub 2/). By considering a special metric geometry with torsion (U/sub 4/) we can describe the duality vector field of a duality invariant Maxwell theory in terms of a special form of torsion. This result indicates that the special U/sub 4/ geometry could play a role in the already unified field theory of Rainich, Misner, and Wheeler (RMW). We show how one could express the RMW conditions, together with their immediate generalizations in terms of geometric objects of the special U/sub 4/ theory. Conformal and projective transformations on the U/sub 4/ connection are examined. It is shown that an appropriate combination of these transformations have the effect of producing a special type of projective transformation on a metric connection with torsion. In the context of a gauge theory based on a U/sub 4/ spacetime, this special type of projective invariance has been interpreted as the underlying invariance principle for baryon number conservation in the same way that gauge changes on the Maxwell vector potential relate to charge conservation.
Decoherence in an interacting quantum field theory: Thermal case
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2011-04-15
We study the decoherence of a renormalized quantum field theoretical system. We consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. Using out-of-equilibrium field theory techniques at finite temperatures, we show that the Gaussian von Neumann entropy for a pure quantum state asymptotes to the interacting thermal entropy. The decoherence rate can be well described by the single particle decay rate in our model. Connecting to electroweak baryogenesis scenarios, we moreover study the effects on the entropy of a changing mass of the system field. Finally, we compare our correlator approach to existing approaches to decoherence in the simple quantum mechanical analogue of our field theoretical model. The entropy following from the perturbative master equation suffers from physically unacceptable secular growth.
Vakonomic Constraints in Higher-Order Classical Field Theory
NASA Astrophysics Data System (ADS)
Campos, Cédric M.
2010-07-01
We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
NASA Astrophysics Data System (ADS)
Román-Roy, Narciso
2009-11-01
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.
Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
NASA Astrophysics Data System (ADS)
de Boer, Jan; Heller, Michal P.; Myers, Robert C.; Neiman, Yasha
2016-02-01
We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher-spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS spacetime.
Quantum κ-deformed differential geometry and field theory
NASA Astrophysics Data System (ADS)
Mercati, Flavio
2016-03-01
I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.
Type II superstring field theory: geometric approach and operadic description
NASA Astrophysics Data System (ADS)
Jurčo, Branislav; Münster, Korbinian
2013-04-01
We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a {N} = 1 generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.
String cosmology — Large-field inflation in string theory
NASA Astrophysics Data System (ADS)
Westphal, Alexander
2015-03-01
This is a short review of string cosmology. We wish to connect string-scale physics as closely as possible to observables accessible to current or near-future experiments. Our possible best hope to do so is a description of inflation in string theory. The energy scale of inflation can be as high as that of Grand Unification (GUT). If this is the case, this is the closest we can possibly get in energy scales to string-scale physics. Hence, GUT-scale inflation may be our best candidate phenomenon to preserve traces of string-scale dynamics. Our chance to look for such traces is the primordial gravitational wave, or tensor mode signal produced during inflation. For GUT-scale inflation this is strong enough to be potentially visible as a B-mode polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale inflation model has a trans-Planckian excursion of the inflaton scalar field during the observable amount of inflation. Such large-field models of inflation have a clear need for symmetry protection against quantum corrections. This makes them ideal candidates for a description in a candidate fundamental theory like string theory. At the same time the need of large-field inflation models for UV completion makes them particularly susceptible to preserve imprints of their string-scale dynamics in the inflationary observables, the spectral index ns and the fractional tensor mode power r. Hence, we will focus this review on axion monodromy inflation as a mechanism of large-field inflation in string theory.
Three-Body Nuclear Systems in Pionless Effective Field Theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared
2016-03-01
New perturbative techniques for three-body systems with contact interactions are discussed. Their application to pionless effective field theory (EF{Tnot π }) for nd scattering is shown, and their extension to bound states addressed. With the extension to bound states a leading-order EF{Tnot π } calculation of the triton charge radius and novel treatments of three-body forces are discussed.
Generating functionals for Green's functions in gauge field theories
Bordag, M.; Kaschlun, L.; Matveev, V.A.; Robaschik, D.
1987-09-01
The structure of the generating functional of the one-particle-irreducible Green's functions in gauge field theories is investigated. Both axial as well as covariant gauge conditions are considered. For both cases, the general structure of the functionals is obtained, and a functional expansion with respect to nonlocal operators is given. The appearance of gauge-dependent operators in the case of the covariant gauge follows in a natural manner from the structure of the corresponding functional.
Approach to non-equilibrium behaviour in quantum field theory
Kripfganz, J.; Perlt, H.
1989-05-01
We study the real-time evolution of quantum field theoretic systems in non-equilibrium situations. Results are presented for the example of scalar /lambda//phi//sup 4/ theory. The degrees of freedom are discretized by studying the system on a torus. Short-wavelength modes are integrated out to one-loop order. The long-wavelength modes considered to be the relevant degrees of freedom are treated by semiclassical phase-space methods. /copyright/ 1989 Academic Press, Inc.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Fodor, Z.; Hoelbling, C.; Katz, S. D.; Lellouch, L.; Portelli, A.; Szabo, K. K.; Toth, B. C.
2016-04-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Horava—Lifshitz Type Quantum Field Theory and Hierarchy Problem
NASA Astrophysics Data System (ADS)
Wei, Chao
2016-06-01
We study the Lifshitz type extension of the standard model (SM) at the UV, with dynamical critical exponent z = 3. One loop radiative corrections to the Higgs mass in such a model are calculated. Our result shows that, the Hierarchy problem, which has initiated many excellent extension of the minimal SM, may be weakened in the z = 3 Lifshitz type quantum field theory. Supported by the National Natural Science Foundation of China
Causal field theory with an infinite speed of sound
Afshordi, Niayesh; Chung, Daniel J. H.; Geshnizjani, Ghazal
2007-04-15
We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.
Quantum to classical transition in quantum field theory
NASA Astrophysics Data System (ADS)
Lombardo, Fernando C.
1998-12-01
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.
Anomalies in non-polynomial closed string field theory
NASA Astrophysics Data System (ADS)
Kaku, Michio
1990-11-01
The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Dual of the Janus solution: An interface conformal field theory
NASA Astrophysics Data System (ADS)
Clark, A. B.; Freedman, D. Z.; Karch, A.; Schnabl, M.
2005-03-01
We propose and study a specific gauge theory dual of the smooth, nonsupersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in Bak et al. [J. High Energy Phys., JHEPFG, 1029-8479 05 (2003) 072]. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary TrX{IXJ} and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g2YM, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value
Quantum field theories in spaces with neutral signatures
NASA Astrophysics Data System (ADS)
Pavšič, Matej
2013-04-01
We point out that quantum field theories based on the concept of Clifford space and Clifford algebra valued-fields involve both positive and negative energies. This is a consequence of the indefinite signature (p, q) of the Clifford space. When the signature is neutral, p = q, then vacuum energy vanishes and there is no cosmological constant problem. A question of the stability of such theories in the presence of interactions arises. We investigate a toy model of the harmonic oscillator in the space M1,1. We have found that in the presence of certain interactions the amplitude of oscillations can remain finite. In general this is not the case and the amplitude grows to infinity, but only when the two frequencies are exactly the same. When they are even slightly different, the amplitude remains finite and the system is stable. We show how such oscillator comes from the Stueckelberg action in curved space, and how it can be generalized to field theories.
Relativistic gravity and parity-violating nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Wu, Chaolun; Wu, Shao-Feng
2015-06-01
We show that the relativistic gravity theory can offer a framework to formulate the nonrelativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2 +1 dimensions which is particularly appropriate for the study on quantum Hall effects and chiral superfluids. We discuss how the nonrelativistic spacetime structure emerges from relativistic gravity. We present covariant maps and constraints that relate the field contents in the two theories, which also serve as the holographic dictionary in the context of gauge/gravity duality. A low energy effective action for fractional quantum Hall states is constructed, which captures universal geometric properties and generates nonuniversal corrections systematically. We give another holographic example with dyonic black brane background to calculate thermodynamic and transport properties of strongly coupled nonrelativistic fluids in magnetic field. In particular, by identifying the shift function in the gravity as a minus of guiding center velocity, we obtain the Hall viscosity with its relation to Landau orbital angular momentum density proportional to Wen-Zee shift. Our formalism has a good projection to lowest Landau level.
Locality of Gravitational Systems from Entanglement of Conformal Field Theories.
Lin, Jennifer; Marcolli, Matilde; Ooguri, Hirosi; Stoica, Bogdan
2015-06-01
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric. PMID:26196612
Gauge transformation of double field theory for open string
NASA Astrophysics Data System (ADS)
Ma, Chen-Te
2015-09-01
We combine symmetry structures of ordinary (parallel directions) and dual (transversal directions) coordinates to construct the Dirac-Born-Infeld theory. The ordinary coordinates are associated with the Neumann boundary conditions and the dual coordinates are associated with the Dirichlet boundary conditions. Gauge fields become scalar fields by exchanging the ordinary and dual coordinates. A gauge transformation of a generalized metric is governed by the generalized Lie derivative. The gauge transformation of the massless closed string theory gives the C -bracket, but the gauge transformation of the open string theory gives the F -bracket. The F -bracket with the strong constraints is different from the Courant bracket by an exact one-form. This exact one-form should come from the one-form gauge field. Based on a symmetry point of view, we deduce a suitable action with a nonzero H -flux at the low-energy level. From an equation of motion of the scalar dilaton, it defines a generalized scalar curvature. Finally, we construct a double sigma model with a boundary term and show that this model with constraints is classically equivalent to the ordinary sigma model.
Multi-time wave functions for quantum field theory
Petrat, Sören; Tumulka, Roderich
2014-06-15
Multi-time wave functions such as ϕ(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.
Locality and entanglement in bandlimited quantum field theory
NASA Astrophysics Data System (ADS)
Pye, Jason; Donnelly, William; Kempf, Achim
2015-11-01
We consider a model for a Planck-scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1 +1 dimensions and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1 +1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.
Locality and entanglement in bandlimited quantum field theory
NASA Astrophysics Data System (ADS)
Pye, Jason; Donnelly, William; Kempf, Achim
We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimensions and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1+1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.
Unifying Self-Consistent Field Theory for Weak Polyelectrolytes
NASA Astrophysics Data System (ADS)
Witte, Kevin; Won, You-Yeon
2008-03-01
A self-consistent field (SCF) theory for weak polyelectrolytes has been derived from a grand canonical partition function. The formalism accounts for the location and mixing of the charged and uncharged polymer species, treating the local (spatially dependent) charge fraction as a field variable with which to minimize the total free energy. This method of the derivation gives the resulting equations, especially those governing the local charge fraction, that are identical to the results obtained by Szleifer and coworkers (J. Polym. Sci. B Polym. Phys., 2006) who built upon the mean-field ``annealed'' free energy expression proposed by Raphael and Joanny (Europhys. Lett., 1990). However, we show that these results are further identical to the ``two-state'' model of Borukhov, Andelman and Orland (Eur. Phys. J. B, 1998), namely, the potential field due to the polymer charges with which the chains interact and the local charge fraction are shown to be exactly equal. This annealed model is derived by averaging the partition function with regard to the monomer charges. The charged and uncharged states are weighted by their probabilities which is, in our notation, the bulk charge fraction and one minus the bulk charge fraction, respectively. The utility of this theory is demonstrated by comparing its predictions against various experimental results from bulk potentiometric measurements and also from polyelectrolyte brush compression studies.
Open string Regge trajectory and its field theory limit
NASA Astrophysics Data System (ADS)
Rojas, Francisco; Thorn, Charles B.
2011-07-01
We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the ’t Hooft limit N→∞ with Ngs2 fixed. Our motivation is to improve the understanding of open string theory at finite α' as a model of gauge field theories. SU(N) gauge theories in D space-time dimensions are described by requiring open strings to end on a stack of N Dp-branes of space-time dimension D=p+1. The large N leading trajectory α(t)=1+α't+Σ(t) can be extracted, through order g2, from the s→-∞ limit, at fixed t, of the four open string tree and planar loop diagrams. We analyze the t→0 behavior with the result that Σ(t)˜-Cg2(-α't)(D-4)/2/(D-4). This result precisely tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D→4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -ln(-α't). We also study Σ(t) in the limit t→-∞ and show that, when D<8, it behaves as α't/(ln(-α't))γ, where γ>0 depends on D and the number of massless scalars. Thus, as long as 4
Reconstruction in quantum field theory with a fundamental length
Soloviev, M. A.
2010-09-15
In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex l-neighborhood of the real space and are localizable at scales large compared to l. The causality condition is formulated as continuity of the field commutator in an appropriate topology associated with the light cone. We prove that the relevant function spaces are nuclear and derive the kernel theorems for the corresponding classes of multilinear functionals, which provides the basis for the reconstruction procedure. Special attention is given to the accurate determination of the domain of the reconstructed quantum fields in the Hilbert space of states. We show that the primitive common invariant domain must be suitably extended to implement the (quasi)localizability and causality conditions.
R&D for the Post-EP Processes of Superconducting RF Cavity
Saeki, Takayuki; Funahashi, Y.; Hayano, H.; Kato, Seigo; Nishiwaki, Michiru; Sawabe, Motoaki; Ueno, Kenji; Watanabe, K.; Antoine, Claire; Berry, Stefurn; Eozenou, F.; Gasser, Y.; Visentin, B.; Clemens, William A.; Geng, Rongli; Manus, Robert; Tyagi, Puneet
2009-11-01
The Electro-Polishing (EP) process is the best candidate of final surface treatment for the production of ILC cavities. Nevertheless, the broad distribution of the gradient caused by field emitters in cavities is sitll a serious problem for the EP process. A candidate source of field emitter is the sulfur component which is produced in the EP process and remains the inner-surface of cavities. We studied the effect of Ethanole- and degreaser-rinse processes after the EP process by a unique method. Moreover, we tried to test the sponge cleaning as the post-EP process to remove the field emitter inside the cavcity. This article describe the results of series tests of the post-EP process at KEK.
Phase-field slip-line theory of plasticity
NASA Astrophysics Data System (ADS)
Freddi, Francesco; Royer-Carfagni, Gianni
2016-09-01
A variational approach to determine the deformation of an ideally plastic substance is proposed by solving a sequence of energy minimization problems under proper conditions to account for the irreversible character of plasticity. The flow is driven by the local transformation of elastic strain energy into plastic work on slip surfaces, once that a certain energetic barrier for slip activation has been overcome. The distinction of the elastic strain energy into spherical and deviatoric parts is used to incorporate in the model the idea of von Mises plasticity and isochoric plastic strain. This is a "phase field model" because the matching condition at the slip interfaces is substituted by the evolution of an auxiliary phase field that, similar to a damage field, is unitary on the elastic phase and null on the yielded phase. The slip lines diffuse in bands, whose width depends upon a material length-scale parameter. Numerical experiments on representative problems in plane strain give solutions with noteworthy similarities with the results from classical slip-line field theory, but the proposed model is much richer because, accounting for elastic deformations, it can describe the formation of slip bands at the local level, which can nucleate, propagate, widen and diffuse by varying the boundary conditions. In particular, the solution for a long pipe under internal pressure is very different from the one obtainable from the classical macroscopic theory of plasticity. For this case, the location of the plastic bands may be an insight to explain the premature failures that are sometimes encountered during the manufacturing process. This practical example enhances the importance of this new theory based on the mathematical sciences.
Field Theory On the World Sheet: Mean Field Expansion And Cutoff Dependence
Bardakci, Korkut; Bardakci, Korkut
2007-01-10
Continuing earlier work, we apply the mean field method to the world sheet representation of a simple field theory. In particular, we study the higher order terms in the mean field expansion, and show that their cutoff dependence can be absorbed into a running coupling constant. The coupling constant runs towards zero in the infrared, and the model tends towards a free string. One cannot fully reach this limit because of infrared problems, however, one can still apply the mean field method to the high energy limit (high mass states) of the string.
The effective field theory of cosmological large scale structures
Carrasco, John Joseph M.; Hertzberg, Mark P.; Senatore, Leonardo
2012-09-20
Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is c^{2}_{s} ≈ 10^{–6}c^{2} and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)^{4}. As a result, the predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k ≃ 0.24h Mpc^{–1}.
Classifying linearly shielded modified gravity models in effective field theory.
Lombriser, Lucas; Taylor, Andy
2015-01-23
We study the model space generated by the time-dependent operator coefficients in the effective field theory of the cosmological background evolution and perturbations of modified gravity and dark energy models. We identify three classes of modified gravity models that reduce to Newtonian gravity on the small scales of linear theory. These general classes contain enough freedom to simultaneously admit a matching of the concordance model background expansion history. In particular, there exists a large model space that mimics the concordance model on all linear quasistatic subhorizon scales as well as in the background evolution. Such models also exist when restricting the theory space to operators introduced in Horndeski scalar-tensor gravity. We emphasize that whereas the partially shielded scenarios might be of interest to study in connection with tensions between large and small scale data, with conventional cosmological probes, the ability to distinguish the fully shielded scenarios from the concordance model on near-horizon scales will remain limited by cosmic variance. Novel tests of the large-scale structure remedying this deficiency and accounting for the full covariant nature of the alternative gravitational theories, however, might yield further insights on gravity in this regime. PMID:25658988
Electromagnetic Form Factors of Hadrons in Quantum Field Theories
Dominguez, C. A.
2008-10-13
In this talk, recent results are presented of calculations of electromagnetic form factors of hadrons in the framework of two quantum field theories (QFT), (a) Dual-Large N{sub c} QCD (Dual-QCD{sub {infinity}}) for the pion, proton, and {delta}(1236), and (b) the Kroll-Lee-Zumino (KLZ) fully renormalizable Abelian QFT for the pion form factor. Both theories provide a QFT platform to improve on naive (tree-level) Vector Meson Dominance (VMD). Dual-QCD{sub {infinity}} provides a tree-level improvement by incorporating an infinite number of zero-width resonances, which can be subsequently shifted from the real axis to account for the time-like behaviour of the form factors. The renormalizable KLZ model provides a QFT improvement of VMD in the framework of perturbation theory. Due to the relative mildness of the {rho}{pi}{pi} coupling, and the size of loop suppression factors, the perturbative expansion is well defined in spite of this being a strong coupling theory. Both approaches lead to considerable improvements of VMD predictions for electromagnetic form factors, in excellent agreement with data.
Is the effective field theory of dark energy effective?
NASA Astrophysics Data System (ADS)
Linder, Eric V.; Sengör, Gizem; Watson, Scott
2016-05-01
The effective field theory of cosmic acceleration systematizes possible contributions to the action, accounting for both dark energy and modifications of gravity. Rather than making model dependent assumptions, it includes all terms, subject to the required symmetries, with four (seven) functions of time for the coefficients. These correspond respectively to the Horndeski and general beyond Horndeski class of theories. We address the question of whether this general systematization is actually effective, i.e. useful in revealing the nature of cosmic acceleration when compared with cosmological data. The answer is no and yes: there is no simple time dependence of the free functions—assumed forms in the literature are poor fits, but one can derive some general characteristics in early and late time limits. For example, we prove that the gravitational slip must restore to general relativity in the de Sitter limit of Horndeski theories, and why it doesn't more generally. We also clarify the relation between the tensor and scalar sectors, and its important relation to observations; in a real sense the expansion history H(z) or dark energy equation of state w(z) is 1/5 or less of the functional information! In addition we discuss the de Sitter, Horndeski, and decoupling limits of the theory utilizing Goldstone techniques.
Renormalized field theory of collapsing directed randomly branched polymers.
Janssen, Hans-Karl; Wevelsiep, Frank; Stenull, Olaf
2009-10-01
We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with epsilon expansion that this transition belongs to the same universality class as directed percolation. PMID:19905335
Scaling Deviations for Neutrino Reactions in Aysmptotically Free Field Theories
DOE R&D Accomplishments Database
Wilczek, F. A.; Zee, A.; Treiman, S. B.
1974-11-01
Several aspects of deep inelastic neutrino scattering are discussed in the framework of asymptotically free field theories. We first consider the growth behavior of the total cross sections at large energies. Because of the deviations from strict scaling which are characteristic of such theories the growth need not be linear. However, upper and lower bounds are established which rather closely bracket a linear growth. We next consider in more detail the expected pattern of scaling deviation for the structure functions and, correspondingly, for the differential cross sections. The analysis here is based on certain speculative assumptions. The focus is on qualitative effects of scaling breakdown as they may show up in the X and y distributions. The last section of the paper deals with deviations from the Callan-Gross relation.
Modifications of the Schwarzschild null geodesics in effective field theories
Ahmadi, N.
2009-12-15
In this paper the dynamics of Schwarzschild null geodesics in the context of low-energy effective field theories incorporating some interactions violating the equivalence principle is examined. Nonperturbed geodesics are expressed in terms of a convenient set of constants called orbital elements. The modifications introduced by the effective interactions are treated as small perturbations, then the method of variation of parameters is employed to find the evolution of the orbital elements for the true worldlines. We next focus our discussion on the geometry of nondispersive photon orbits and highlight the importance of different orbital elements in long-term change of the orbit. This calculation shows that nondispersive forces acting on null geodesics drive a secular growth of the positional elements. As an application of our results we examine the evolution of mean orbital elements in the semiclassical theory of quantum gravitational optics and show that the averaged correction terms are within the range of the uncertainty principle.
Synchrotron radiation in strongly coupled conformal field theories
Athanasiou, Christiana; Chesler, Paul M.; Liu, Hong; Rajagopal, Krishna; Nickel, Dominik
2010-06-15
Using gauge/gravity duality, we compute the energy density and angular distribution of the power radiated by a quark undergoing circular motion in strongly coupled N=4 supersymmetric Yang-Mills theory. We compare the strong coupling results to those at weak coupling, finding them to be very similar. In both regimes, the angular distribution of the radiated power is in fact similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle {alpha}{approx}1/{gamma}. To an observer far away from the quark, the emitted radiation appears as a short periodic burst, just like the light from a lighthouse does to a ship at sea. Our strong coupling results are valid for any strongly coupled conformal field theory with a dual classical gravity description.
Energy flux positivity and unitarity in conformal field theories.
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-01
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux. PMID:21231731
Energy Flux Positivity and Unitarity in Conformal Field Theories
Kulaxizi, Manuela; Parnachev, Andrei
2011-01-07
We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop light like poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-free is equivalent to the condition of positivity of energy flux.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry. PMID:23909305
Quantum field theory of van der Waals friction
Volokitin, A. I.; Persson, B. N. J.
2006-11-15
van der Waals friction between two semi-infinite solids, and between a small neutral particle and semi-infinite solid is studied using thermal quantum field theory in the Matsubara formulation. We show that the friction to linear order in the sliding velocity can be obtained from the equilibrium Green functions and that our treatment can be extended for bodies with complex geometry. The calculated friction agrees with the friction obtained using a dynamical modification of the Lifshitz theory, which is based on the fluctuation-dissipation theorem. We show that it should be possible to measure the van der Waals friction in noncontact friction experiment using state-of-the-art equipment.
Action and entanglement in gravity and field theory.
Neiman, Yasha
2013-12-27
In nongravitational quantum field theory, the entanglement entropy across a surface depends on the short-distance regularization. Quantum gravity should not require such regularization, and it has been conjectured that the entanglement entropy there is always given by the black hole entropy formula evaluated on the entangling surface. We show that these statements have precise classical counterparts at the level of the action. Specifically, we point out that the action can have a nonadditive imaginary part. In gravity, the latter is fixed by the black hole entropy formula, while in nongravitating theories it is arbitrary. From these classical facts, the entanglement entropy conjecture follows by heuristically applying the relation between actions and wave functions. PMID:24483789
Towards Noncommutative Topological Quantum Field Theory - Hodge theory for cyclic cohomology
NASA Astrophysics Data System (ADS)
Zois, I. P.
2014-03-01
Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation.
Nonlinear density fluctuation field theory for large scale structure
NASA Astrophysics Data System (ADS)
Zhang, Yang; Miao, Hai-Xing
2009-05-01
We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuations up to second order, we obtain the nonlinear field equation of 2-pt correlation ξ(r), which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and mass renormalization, the equation becomes closed with two new terms beyond the Gaussian approximation, and their coefficients are taken as parameters. The analytic solution is obtained in terms of the hypergeometric functions, which is checked numerically. With one single set of two fixed parameters, the correlation ξ(r) and the corresponding power spectrum P(κ) simultaneously match the results from all the major surveys, such as APM, SDSS, 2dfGRS, and REFLEX. The model gives a unifying understanding of several seemingly unrelated features of large scale structure from a field-theoretical perspective. The theory is worth extending to study the evolution effects in an expanding universe.
Perturbations of single-field inflation in modified gravity theory
NASA Astrophysics Data System (ADS)
Qiu, Taotao; Xia, Jun-Qing
2015-05-01
In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form f (R). Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure f (R) theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there is large parameter space in these models, we show that it is easy to fit the data very well.
Construction of Quantum Field Theories with Factorizing S-Matrices
NASA Astrophysics Data System (ADS)
Lechner, Gandalf
2008-02-01
A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyzed with operator-algebraic techniques, in particular by using the modular nuclearity condition of Buchholz, d’Antoni and Longo. Besides a model-independent result regarding the Reeh Schlieder property of the vacuum in this framework, an infinite class of quantum field theoretic models with non-trivial interaction is constructed. This construction completes a program initiated by Schroer in a large family of theories, a particular example being the Sinh-Gordon model. The crucial problem of establishing the existence of local observables in these models is solved by verifying the modular nuclearity condition, which here amounts to a condition on analytic properties of form factors of observables localized in wedge regions. It is shown that the constructed models solve the inverse scattering problem for the considered class of S-matrices. Moreover, a proof of asymptotic completeness is obtained by explicitly computing total sets of scattering states. The structure of these collision states is found to be in agreement with the heuristic formulae underlying the Zamolodchikov-Faddeev algebra.
The application of mean field theory to image motion estimation.
Zhang, J; Hanauer, G G
1995-01-01
Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates. PMID:18289956
Exotic Bbb R4 and quantum field theory
NASA Astrophysics Data System (ADS)
Asselmeyer-Maluga, Torsten; Mader, Roland
2012-02-01
Recent work on exotic smooth Bbb R4,s, i.e. topological Bbb R4 with exotic differential structure, shows the connection of 4-exotics with the codimension-1 foliations of S3, SU(2) WZW models and twisted K-theory KH(S3), H in H3(S3,Bbb Z). These results made it possible to explicate some physical effects of exotic 4-smoothness. Here we present a relation between exotic smooth Bbb R4 and operator algebras. The correspondence uses the leaf space of the codimension-1 foliation of S3 inducing a von Neumann algebra W(S3) as description. This algebra is a type III1 factor lying at the heart of any observable algebra of QFT. By using the relation to factor II, we showed that the algebra W(S3) can be interpreted as Drinfeld-Turaev deformation quantization of the space of flat SL(2, Bbb C) connections (or holonomies). Thus, we obtain a natural relation to quantum field theory. Finally we discuss the appearance of concrete action functionals for fermions or gauge fields and its connection to quantum-field-theoretical models like the Tree QFT of Rivasseau.
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Primordial statistical anisotropies: the effective field theory approach
NASA Astrophysics Data System (ADS)
Akbar Abolhasani, Ali; Akhshik, Mohammad; Emami, Razieh; Firouzjahi, Hassan
2016-03-01
In this work we present the effective field theory of primordial statistical anisotropies generated during anisotropic inflation involving a background U(1) gauge field. Besides the usual Goldstone boson associated with the breaking of time diffeomorphism we have two additional Goldstone bosons associated with the breaking of spatial diffeomorphisms. We further identify these two new Goldstone bosons with the expected two transverse degrees of the U(1) gauge field fluctuations. Upon defining the appropriate unitary gauge, we present the most general quadratic action which respects the remnant symmetry in the unitary gauge. The interactions between various Goldstone bosons leads to statistical anisotropy in curvature perturbation power spectrum. Calculating the general results for power spectrum anisotropy, we recover the previously known results in specific models of anisotropic inflation. In addition, we present novel results for statistical anisotropy in models with non-trivial sound speed for inflaton fluctuations. Also we identify the interaction which leads to birefringence-like effects in anisotropic power spectrum in which the speed of gauge field fluctuations depends on the direction of the mode propagation and the two polarization of gauge field fluctuations contribute differently in statistical anisotropy. As another interesting application, our EFT approach naturally captures interactions generating parity violating statistical anisotropies.
On a gauge covariant formulation of string field theories
NASA Astrophysics Data System (ADS)
Ju-Fei, Tang; Chuan-Jie, Zhu
1986-11-01
It is shown that the Neveu-Nicolai-West formulation of the gauge covariant string field theories and that of Banks and Peskin can be obtained by different consistent truncation of the BRST multiplets. A proof is given to show the equivalence of light-cone formulation and the gauge covariant formulation without using the property of trivial cohomology of string differential forms. We would like to thank D.D. Wu and X.J. Zhou for discussion and Yi-Bing Ding for careful reading of the manuscript.
Three-body systems in pionless effective field theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared
2016-04-01
Investigations of three-body nuclear systems using pionless effective field theory (EFTπ̸) are reviewed. The history of EFTπ̸ in nd and pd scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in pd scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in nd scattering are also considered and the utility of EFTπ̸ for addressing them.
Limits on Higgs boson couplings in Effective field theory
NASA Astrophysics Data System (ADS)
Belyaev, N.; Reid, T.
2016-02-01
We review the Effective Field Theory (EFT) to make projections on physics beyond the Standard Model in the Higgs sector. We provide relations between the non-Standard Model couplings of the Strongly-Interacting Light Higgs (SILH) effective Lagrangian implemented in the eHDecay package and the corresponding terms of the spin-0 Higgs Characterisation model's effective Lagrangian used with the aMC@NLO Monte Carlo generator. Constraints on BSM couplings are determined on the basis of existing experimental limits on Higgs boson width and branching ratios.
Effective field theory for nuclear vibrations with quantified uncertainties
NASA Astrophysics Data System (ADS)
Coello Pérez, E. A.; Papenbrock, T.
2015-12-01
We develop an effective field theory (EFT) for nuclear vibrations. The key ingredients—quadrupole degrees of freedom, rotational invariance, and a breakdown scale around the three-phonon level—are taken from data. The EFT is developed for spectra and electromagnetic moments and transitions. We employ tools from Bayesian statistics for the quantification of theoretical uncertainties. The EFT consistently describes spectra and electromagnetic transitions for 62Ni,100,98Ru,108,106Pd, 110,112,114Cd, and 118,120,122Te within the theoretical uncertainties. This suggests that these nuclei can be viewed as anharmonic vibrators.
Spin and orbital exchange interactions from Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.
2016-02-01
We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.
Mean-field theory of planar absorption of RNA molecules
NASA Astrophysics Data System (ADS)
Nguyen, Toan; Bruinsma, Robijn; Gelbart, William
2006-03-01
Interaction between the viral RNA and the protective protein capsid plays a very important role in the cell infection and self-assembly process of a virus. To better understand this interaction, we study a similar problem of absorption of RNA on an attractive wall. It is known that the secondary structure of a folded RNA molecules without pseudo-knots has the same topology as that of a branched polymer. We use a mean-field theory for branched polymers to analytically calculate the RNA concentration profile. The results are compared to known exact scaling calculations and computer simulations.
Effective field theory of dark matter from membrane inflationary paradigm
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan; Dasgupta, Arnab
2016-09-01
In this article, we have studied the cosmological and particle physics constraints on dark matter relic abundance from effective field theory of inflation from tensor-to-scalar ratio (r), in case of Randall-Sundrum single membrane (RSII) paradigm. Using semi-analytical approach we establish a direct connection between the dark matter relic abundance (ΩDMh2) and primordial gravity waves (r), which establishes a precise connection between inflation and generation of dark matter within the framework of effective field theory in RSII membrane. Further assuming the UV completeness of the effective field theory perfectly holds good in the prescribed framework, we have explicitly shown that the membrane tension, σ ≤ O(10-9) Mp4, bulk mass scale M5 ≤ O(0.04 - 0.05) Mp, and cosmological constant Λ˜5 ≥ - O(10-15) Mp5, in RSII membrane plays the most significant role to establish the connection between dark matter and inflation, using which we have studied the features of various mediator mass scale suppressed effective field theory "relevant operators" induced from the localized s, t and u channel interactions in RSII membrane. Taking a completely model independent approach, we have studied an exhaustive list of tree-level Feynman diagrams for dark matter annihilation within the prescribed setup and to check the consistency of the obtained results, further we apply the constraints as obtained from recently observed Planck 2015 data and Planck + BICEP2 + Keck Array joint data sets. Using all of these derived results we have shown that to satisfy the bound on, ΩDMh2 = 0.1199 ± 0.0027, as from Planck 2015 data, it is possible to put further stringent constraint on r within, 0.01 ≤ r ≤ 0.12, for thermally averaged annihilation cross-section of dark matter, < σv > ≈ O(10-28 - 10-27) cm3 / s, which are very useful to constrain various membrane inflationary models.
Collective field theory of a singular supersymmetric matrix model
de Mello Koch, R.; Rodrigues, J.P.
1995-05-15
The supersymmetric collective field theory with the potential {ital v}{prime}({ital x})={omega}{ital x}{minus}{eta}/{ital x} is studied. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeroes of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a Majorana fermion. The {ital x} space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
Hadron Structures from Large Momentum Effective Field Theory
NASA Astrophysics Data System (ADS)
Xiong, Xiaonu
2016-08-01
The large momentum effective field theory (LaMET) is aiming to calculate parton distributions directly on lattice. In this approach a class of so-called quasi distributions are defined as pure spatial correlations in a finite momentum frame and they are directly calculated on lattice. The light-cone distributions are extracted from the quasi distributions by perturbative matching conditions. We present the application of LaMET on parton distribution functions and generalized parton distributions. Besides, heavy meson's quasi and light-cone distribution amplitudes are studied under nonrelativistic QCD (NRQCD) factorization framework.
Atomistic force field for alumina fit to density functional theory
Sarsam, Joanne; Finnis, Michael W.; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al{sub 2}O{sub 3}), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
Applicability of self-consistent mean-field theory
Guo Lu; Sakata, Fumihiko; Zhao Enguang
2005-02-01
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case.
Traveling wave solution of the Reggeon field theory
Peschanski, Robi
2009-05-15
We identify the nonlinear evolution equation in impact-parameter space for the 'Supercritical Pomeron' in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy traveling wave solution corresponding to a 'universal' behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.
Mean-field theory of a recurrent epidemiological model.
Nagy, Viktor
2009-06-01
Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity. PMID:19658562
Mean-field theory of a recurrent epidemiological model
NASA Astrophysics Data System (ADS)
Nagy, Viktor
2009-06-01
Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Design of traveling wave tubes based on field theory
Vanderplaats, N.R.; Kodis, M.A. . Vacuum Electronics Branch); Freund, H.P. )
1994-07-01
A method is described for the design of helix traveling wave tubes (TWT) which is based on the linear field analysis of the coupled beam-wave system. The dispersion relations are obtained by matching of radial admittances at boundaries instead of the individual field components. This approach provides flexibility in modeling various beam and circuit configurations with relative ease by choosing the appropriate admittance functions for each case. The method is illustrated for the case of a solid beam inside a sheath helix which is loaded externally by lossy dielectric material, a conducting cylinder, and axial vanes. Extension of the analysis to include a thin tape helix model is anticipated in the near future. The TWT model may be divided into axial regions to include velocity tapers, lossy materials and severs, with the helix geometry in each region varied arbitrarily. The relations between the ac velocities, current densities, and axial electric fields are used to derive a general expression for the new amplitudes of the three forward waves at each axial boundary. The sum of the fields for the three forward waves (two waves in a drift region) is followed to the circuit output. Numerical results of the field analysis are compared with the coupled-mode Pierce theory. A method is suggested for applying the field analysis to accurate design of practical TWT's that have a more complex circuit geometry, which starts with a simple measurement of the dispersion of the helix circuit. The field analysis may then be used to generate a circuit having properties very nearly equivalent to those of the actual circuit.
Dynamic scattering theory for dark-field electron holography of 3D strain fields.
Lubk, Axel; Javon, Elsa; Cherkashin, Nikolay; Reboh, Shay; Gatel, Christophe; Hÿtch, Martin
2014-01-01
Dark-field electron holography maps strain in crystal lattices into reconstructed phases over large fields of view. Here we investigate the details of the lattice strain-reconstructed phase relationship by applying dynamic scattering theory both analytically and numerically. We develop efficient analytic linear projection rules for 3D strain fields, facilitating a straight-forward calculation of reconstructed phases from 3D strained materials. They are used in the following to quantify the influence of various experimental parameters like strain magnitude, specimen thickness, excitation error and surface relaxation. PMID:24012934
Trivial pursuits: studies in quantum field theory and squantum cosmology
Furlong, R.C.
1987-01-01
The author show that the nonrelativistic limit of the lambdaphi/sup 4/ theory is trivial in 1 + 3 dimensions; the renormalized coupling constant vanishes and the S matrix reduces to the unit matrix. Our result is consistent with, though not sufficient to establish, the triviality of the Lorentz-invariant theory. A necessary condition for the existence of a consistent non-trivial continuum quantum field theory in d = 4 is the existence of an ultraviolet-stable fixed point of the Gell-Mann-Low renormalization group. Since others have shown (non-perturbatively) that the existence of just such a fixed point is sufficient to guarantee the triviality of the continuum massless Wess-Zumino model, we conclude that this model cannot exist non-trivially in d = 4. The fact that most renormalization group blocking schemes include each site link in many block links can generate spurious interactions in the block system. A general method for avoiding this problem is formulated and applied to do a Monte Carlo renormalization group study of the SU(2)-Higgs model in four dimensions with a check 2 scale factor. Finally starting from the D'Eath equation, the Dirac square root of the Wheeler-De Witt equation, for N = 1 supergravity, we construct superminisuperspace models (and quasi-models) for supersymmetric quantum cosmology (squantum cosmology) compatibile with Friedmann-Robertson-Walker (FRW) cosmologies.
Bias in the effective field theory of large scale structures
Senatore, Leonardo
2015-11-05
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. Furthermore, we describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/k_{NL} and k/k_{M}, where k is the wavenumber of interest, k_{NL} is the wavenumber associated to the non-linear scale, and k_{M} is the comoving wavenumber enclosing the mass of a galaxy.
Bias in the effective field theory of large scale structures
Senatore, Leonardo
2015-11-05
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local inmore » space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. Furthermore, we describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/kNL and k/kM, where k is the wavenumber of interest, kNL is the wavenumber associated to the non-linear scale, and kM is the comoving wavenumber enclosing the mass of a galaxy.« less
Universal behavior after a quantum quench in interacting field theories
NASA Astrophysics Data System (ADS)
Mitra, Aditi
The dynamics of an isolated quantum system represented by a field theory with O(N) symmetry, and in d>2 spatial dimensions, is investigated after a quantum quench from a disordered initial state to the critical point. A perturbative renormalization-group approach involving an expansion around d=4 is employed to study the time-evolution, and is supplemented by an exact solution of the Hartree-Fock equations in the large-N limit. The results show that the dynamics is characterized by a prethermal regime controlled by elastic dephasing where excitations propagate ballistically, and a light cone emerges in correlation functions in real space. The memory of the initial state, together with the absence of time-scales at the critical point, gives rise to universal power-law aging which is characterized by a new non-equilibrium short-time exponent. The dynamics of the entanglement following a quench is also explored, and reveals that while the time evolution of the entanglement entropy itself is not much different between a free bosonic theory and an interacting bosonic theory, the low-energy entanglement spectrum on the other hand shows clear signature of the non-equilibrium short-time exponent related to aging. This work was done in collaboration with Y. Lemonik (NYU), M. Tavora (NYU), A. Chiocchetta (SISSA), A. Maraga (SISSA), and A. Gambassi (SISSA). Supported by NSF-DMR 1303177.
Bias in the effective field theory of large scale structures
NASA Astrophysics Data System (ADS)
Senatore, Leonardo
2015-11-01
We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/kNL and k/kM, where k is the wavenumber of interest, kNL is the wavenumber associated to the non-linear scale, and kM is the comoving wavenumber enclosing the mass of a galaxy.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
NASA Astrophysics Data System (ADS)
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
Multiagent model and mean field theory of complex auction dynamics
NASA Astrophysics Data System (ADS)
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
2015-09-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
Effective field theory of thermal Casimir interactions between anisotropic particles
NASA Astrophysics Data System (ADS)
Haussman, Robert C.; Deserno, Markus
2014-06-01
We employ an effective field theory (EFT) approach to study thermal Casimir interactions between objects bound to a fluctuating fluid surface or interface dominated by surface tension, with a focus on the effects of particle anisotropy. The EFT prescription disentangles the constraints imposed by the particles' boundaries from the calculation of the interaction free energy by constructing an equivalent point particle description. The finite-size information is captured in a derivative expansion that encodes the particles' response to external fields. The coefficients of the expansion terms correspond to generalized tensorial polarizabilities and are found by matching the results of a linear response boundary value problem computed in both the full and effective theories. We demonstrate the versatility of the EFT approach by constructing the general effective Hamiltonian for a collection of particles of arbitrary shapes. Taking advantage of the conformal symmetry of the Hamiltonian, we discuss a straightforward conformal mapping procedure to systematically determine the polarizabilities and derive a complete description for elliptical particles. We compute the pairwise interaction energies to several orders for nonidentical ellipses as well as their leading-order triplet interactions and discuss the resulting preferred pair and multibody configurations. Furthermore, we elaborate on the complications that arise with pinned particle boundary conditions and show that the powerlike corrections expected from dimensional analysis are exponentially suppressed by the leading-order interaction energies.
No-go theorems for generalized chameleon field theories.
Wang, Junpu; Hui, Lam; Khoury, Justin
2012-12-14
The chameleon, or generalizations thereof, is a light scalar that couples to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: (i) the Compton wavelength of such a scalar can be at most ~/= 1 MPc at the present cosmic density, which restricts its impact to nonlinear scales; and (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time, which precludes the possibility of self-acceleration. These results imply that chameleonlike scalar fields have a negligible effect on the linear-scale growth history; theories that invoke a chameleonlike scalar to explain cosmic acceleration rely on a form of dark energy rather than a genuine modified gravity effect. Our analysis applies to a broad class of chameleon, symmetron, and dilaton theories. PMID:23368302
The effectiveness of mean-field theory for avalanche distributions
NASA Astrophysics Data System (ADS)
Lee, Edward; Raju, Archishman; Sethna, James
We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.
Effective field theory of thermal Casimir interactions between anisotropic particles.
Haussman, Robert C; Deserno, Markus
2014-06-01
We employ an effective field theory (EFT) approach to study thermal Casimir interactions between objects bound to a fluctuating fluid surface or interface dominated by surface tension, with a focus on the effects of particle anisotropy. The EFT prescription disentangles the constraints imposed by the particles' boundaries from the calculation of the interaction free energy by constructing an equivalent point particle description. The finite-size information is captured in a derivative expansion that encodes the particles' response to external fields. The coefficients of the expansion terms correspond to generalized tensorial polarizabilities and are found by matching the results of a linear response boundary value problem computed in both the full and effective theories. We demonstrate the versatility of the EFT approach by constructing the general effective Hamiltonian for a collection of particles of arbitrary shapes. Taking advantage of the conformal symmetry of the Hamiltonian, we discuss a straightforward conformal mapping procedure to systematically determine the polarizabilities and derive a complete description for elliptical particles. We compute the pairwise interaction energies to several orders for nonidentical ellipses as well as their leading-order triplet interactions and discuss the resulting preferred pair and multibody configurations. Furthermore, we elaborate on the complications that arise with pinned particle boundary conditions and show that the powerlike corrections expected from dimensional analysis are exponentially suppressed by the leading-order interaction energies. PMID:25019720
Effective field theory for Higgs boson plus jet production
NASA Astrophysics Data System (ADS)
Dawson, S.; Lewis, I. M.; Zeng, Mao
2014-11-01
We use an effective field theory which includes all possible gluon-Higgs dimension-5 and dimension-7 operators to study Higgs boson plus jet production in next-to-leading order QCD. The effective field theory sheds light on the effect of a finite top quark mass as well as any beyond-the-Standard-Model modifications of Higgs-gluon effective couplings. In the gluon channel, the accuracy of the heavy-top approximation for differential distributions arises from the noninterference between the helicity amplitudes of the G3h and G2h operators in the mh
Dynamical renormalization group approach to relaxation in quantum field theory
NASA Astrophysics Data System (ADS)
Boyanovsky, D.; de Vega, H. J.
2003-10-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.
Unified Field Theory and Force Formulas of Interactions
NASA Astrophysics Data System (ADS)
Ma, Tian; Wang, Shouhong
2013-04-01
The main objective of this talk is to drive a unified field model coupling four interactions, based on the principle of interaction dynamics (PID) and the principle of representation invariance (PID). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint. PRI requires that physical laws be independent of representations of the gauge groups. One important outcome of this unified field model is a natural duality between the interacting fields (g, A, W^a, S^k), corresponding to graviton, photon, intermediate vector bosons W^± and Z and gluons, and the adjoint bosonic fields (φ,, ^aw, ^ks). This duality predicts two Higgs particles of similar mass with one due to weak interaction and the other due to strong interaction. PID and PRI can be applied directly to individual interactions, leading to 1) modified Einstein equations, giving rise to a unified theory for dark matter and dark energy, 2) three levels of strong interaction potentials for quark, nucleon/hadron, and atom respectively, and 3) a weak interaction potential. These potential/force formulas offer a clear mechanism for both quark confinement and asymptotic freedom.
Topological Effective Field Theories for Dirac Fermions from Index Theorem
NASA Astrophysics Data System (ADS)
Palumbo, Giandomenico; Catenacci, Roberto; Marzuoli, Annalisa
2014-01-01
Dirac fermions have a central role in high energy physics but it is well-known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1)-massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. The first step of our strategy is standard (in the Hermitian case) and consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization. Then, we introduce a suitable splitting of the heat kernel that naturally selects the purely topological part of the determinant (i.e., the topological effective action). This topological effective action is expressed in terms of gauge fields using the Atiyah-Singer index theorem which computes the analytical index in topological terms. The main new result of this paper is to provide a consistent extension of this method to the non-Hermitian case, where a well-defined determinant does not exist. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories (TEFTs).
Archer, A J; Evans, R
2013-01-01
The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT. PMID:23298050
Effective field theory for quantum liquid in dwarf stars
Gabadadze, Gregory; Rosen, Rachel A. E-mail: rarosen@physik.su.se
2010-04-01
An effective field theory approach is used to describe quantum matter at greater-than-atomic but less-than-nuclear densities which are encountered in white dwarf stars. We focus on the density and temperature regime for which charged spin-0 nuclei form an interacting charged Bose-Einstein condensate, while the neutralizing electrons form a degenerate fermi gas. After a brief introductory review, we summarize distinctive properties of the charged condensate, such as a mass gap in the bosonic sector as well as gapless fermionic excitations. Charged impurities placed in the condensate are screened with great efficiency, greater than in an equivalent uncondensed plasma. We discuss a generalization of the Friedel potential which takes into account bosonic collective excitations in addition to the fermionic excitations. We argue that the charged condensate could exist in helium-core white dwarf stars and discuss the evolution of these dwarfs. Condensation would lead to a significantly faster rate of cooling than that of carbon- or oxygen-core dwarfs with crystallized cores. This prediction can be tested observationally: signatures of charged condensation may have already been seen in the recently discovered sequence of helium-core dwarfs in the nearby globular cluster NGC 6397. Sufficiently strong magnetic fields can penetrate the condensate within Abrikosov-like vortices. We find approximate analytic vortex solutions and calculate the values of the lower and upper critical magnetic fields at which vortices are formed and destroyed respectively. The lower critical field is within the range of fields observed in white dwarfs, but tends toward the higher end of this interval. This suggests that for a significant fraction of helium-core dwarfs, magnetic fields are entirely expelled within the core.
Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
NASA Astrophysics Data System (ADS)
Kita, T.
2010-04-01
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keld ysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Phi-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Phi-derivable approximation, i.e., an issue of how to handle the ``Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy''. Aim (ii) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems ca n be handled
Perturbative quantum field theory in the framework of the fermionic projector
Finster, Felix
2014-04-15
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Geometrical Effective Action: Gauge Field Theory Without Ghosts.
NASA Astrophysics Data System (ADS)
Paris, Carmen Molina
Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph. Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions^1, obtaining thereby a mode sum over tree functions. It is easy to show that tree functions are gauge invariant provided the external lines bear only physical mode functions. Feynman therefore proposed to restrict the mode sums to physical modes, a procedure that not only secures gauge invariance but unitarity as well. But there is a difficulty: Because the physical mode functions are defined in a special frame, the procedure is not manifestly Lorentz invariant ^2. Feynman was able to show that deletion of the nonphysical modes is equivalent to subtracting, from the contribution of every closed loop, that of another (Lorentz invariant) loop propagating a particle having spin 1 (or one less than that of the gauge field). This is the ghost. Because its contribution is subtracted, it is a fermion. Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show
EPS cautions against budget cuts
NASA Astrophysics Data System (ADS)
Stafford, Ned
2015-03-01
The European Physical Society (EPS) has hit out at plans to remove €2.7bn from the €80bn budget of Horizon 2020 - the European Union's main research funding programme - and use the money instead to help finance a new European Union economic-stimulus initiative.
Tunneling in quantum field theory and semiclassical gravity
NASA Astrophysics Data System (ADS)
Wohns, Dan Funch
In this dissertation we discuss aspects of the transitions between metastable vacua in scalar field theories. These transitions are caused by nucleation of bubbles of one vacuum in a background of another vacuum, and may have relevance in cosmology. Such processes are typically exponentially suppressed in the height and width of the barriers between the vacua. We demonstrate several scenarios where this intuition fails. We use a functional Schrodinger approach to show that tunneling of a scalar field through two barriers can be exponentially faster than tunneling through a single barrier. We determine the conditions that the effective potential must satisfy for a large enhancement in the tunneling rate to be possible. Both the tunneling rate to nearby vacua and to distant vacua in field space can be enhanced by this process. It may be possible to test this phenomenon using superfluid Helium-3. Nucleation of the B phase in samples of the supercooled A phase of superfluid Helium-3 is observed in seconds or minutes, while the characteristic decay time is calculated to be longer than the age of the universe. We propose a resolution to this discrepancy using resonant tunneling. This explanation makes the distinctive prediction that there exist multiple peaks in the nucleation probability as a function of temperature, pressure, and magnetic field. Next we investigate in detail Coleman-de Luccia tunneling. We show that there are four types of tunneling, depending on the importance of thermal and horizon effects. We estimate corrections to the Hawking-Moss tunneling rate, which can be large. Finally, the tunneling rate for a scalar field described by the Dirac-Born-Infeld action is calculated in the Hawking-Moss limit using a stochastic approach.
Topics in brane world and quantum field theory
NASA Astrophysics Data System (ADS)
Corradini, Olindo
In the first part of the thesis we study various issues in the Brane World scenario with particular emphasis on gravity and the cosmological constant problem. First, we study localization of gravity on smooth domain-wall solutions of gravity coupled to a scalar field. In this context we discuss how the aforementioned localization is affected by including higher curvature terms in the theory, pointing out among other things that, general combinations of such terms lead to delocalization of gravity with the only exception of the Gauss-Bonnet combination (and its higher dimensional counterparts). We then find a solitonic 3-brane solution in 6D bulk in the Einstein-Hilbert-Gauss-Bonnet theory of gravity. Near to the brane the metric is that for a product of the 4D flat Minkowski space with a 2D wedge whose deficit angle is proportional to the brane tension. Consistency tests imposed on such backgrounds appear to require the localized matter on the brane to be conformal. We then move onto infinite volume extra dimension Brane World scenarios where we study gravity in a codimension-2 model, generalizing the work of Dvali, Gabadadze and Porrati to tensionful branes. We point out that, in the presence of the bulk Gauss-Bonnet combination, the Einstein-Hilbert term is induced on the brane already at the classical level. Consistency tests are presented here as well. To conclude we discuss, using String Theory, an interesting class of large-N gauge theories which have vanishing energy density even though these theories are non-covariant and non-supersymmetric. In the second part of the thesis we study a formulation of Quantum Mechanical Path Integrals in curved space. Such Path Integrals present superficial divergences which need to be regulated. We perform a three-loop calculation in mode regularization as a nontrivial check of the non-covariant counterterms required by such scheme. We discover that dimensional regularization can be successfully adopted to evaluate the
On evaluation of nonplanar diagrams in noncommutative field theory
NASA Astrophysics Data System (ADS)
Liao, Yi
2005-05-01
This is a technical work about how to evaluate loop integrals appearing in one loop nonplanar (NP) diagrams in noncommutative (NC) field theory. The conventional wisdom says that, barring the ultraviolet/infrared (UV/IR) mixing problem, NP diagrams whose planar counterparts are UV divergent are rendered finite by NC phases that couple the loop momentum to the external ones p through an NC momentum ρ=θp. We show that this is generally not the case. We find that subtleties arise already in the simpler case of Euclidean spacetime. The situation is even worse in Minkowski spacetime due to its indefinite metric. We compare different prescriptions that may be used to evaluate loop integrals in ordinary theory. They are equivalent in the sense that they always yield identical results. However, in NC theory there is no a priori reason that these prescriptions, except for the defining one that is built in the Feynman propagator, are physically justified even when they seem mathematically meaningful. Employing them can lead to ambiguous results, which are also different from those obtained according to the defining prescription. For ρ>0, the NC phase can worsen the UV property of loop integrals instead of always improving it in high dimensions. We explain how this surprising phenomenon comes about from the indefinite metric. This lends a strong support to the point of view that the naive approach is not well-founded when time does not commute with space. For ρ<0, the NC phase improves the UV property and softens the quadratic UV divergence in ordinary theory to a bounded but indefinite UV oscillation. We employ a cut-off method to quantify the new UV nonregular terms. For ρ>0, these terms are generally complex and thus also harm unitarity in addition to those found previously. As the new terms for both cases are not available in the Lagrangian and in addition can be non-Hermitian when time does not commute with space, our result casts doubts on previous demonstrations
Neural networks, field theory, directed percolation, and critical branching
NASA Astrophysics Data System (ADS)
Buice, Michael A.
We describe the dynamics of neural activity using field-theoretic methods for non-equilibrium statistical processes. Using a Markov assumption, we introduce the "spike model". The spike model permits a characterization of both neural fluctuations and response, presenting a tractable way to extend the mean field (Wilson-Cowan) equations used in much of theoretical and computational neuroscience. We also demonstrate the formalism's application to the Cowan models, one of which is equivalent to the forest fire model with immune trees. We argue that neural activity under mild conditions exhibits a dynamical phase transition which is in the universality class of directed percolation (DP). Owing to the spatial extent of neural interactions, there is a region in which the critical behavior is that of a branching process before crossing over into the DP region, consistent with measurements in cortical slice preparations. From the perspective of theoretical neuroscience, a principal contribution of this work is the connection of the problem of non-linear, non-Gaussian systems with the problem of dealing with infrared singularities in field theory. This work suggests a general characterization of epilepsy as a manifestation of a directed percolation phase transition.
Effective field theory of non-attractor inflation
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra
2015-07-29
We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.
Improved routing strategy based on gravitational field theory
NASA Astrophysics Data System (ADS)
Song, Hai-Quan; Guo, Jin
2015-10-01
Routing and path selection are crucial for many communication and logistic applications. We study the interaction between nodes and packets and establish a simple model for describing the attraction of the node to the packet in transmission process by using the gravitational field theory, considering the real and potential congestion of the nodes. On the basis of this model, we propose a gravitational field routing strategy that considers the attractions of all of the nodes on the travel path to the packet. In order to illustrate the efficiency of proposed routing algorithm, we introduce the order parameter to measure the throughput of the network by the critical value of phase transition from a free flow phase to a congested phase, and study the distribution of betweenness centrality and traffic jam. Simulations show that, compared with the shortest path routing strategy, the gravitational field routing strategy considerably enhances the throughput of the network and balances the traffic load, and nearly all of the nodes are used efficiently. Project supported by the Technology and Development Research Project of China Railway Corporation (Grant No. 2012X007-D) and the Key Program of Technology and Development Research Foundation of China Railway Corporation (Grant No. 2012X003-A).
NASA Astrophysics Data System (ADS)
Peskin, Michael E.
2011-04-01
Anthony Zee is not only a leading theoretical physicist but also an author of popular books on both physics and non-physics topics. I recommend especially `Swallowing Clouds', on Chinese cooking and its folklore. Thus, it is not surprising that his textbook has a unique flavor. Derivations end, not with `QED' but with exclamation points. At the end of one argument, we read `Vive Cauchy!', in another `the theorem practically exudes generality'. This is quantum field theory taught at the knee of an eccentric uncle; one who loves the grandeur of his subject, has a keen eye for a slick argument, and is eager to share his repertoire of anecdotes about Feynman, Fermi, and all of his heroes. A one-page section entitled `Electric Charge' illustrates the depth and tone of the book. In the previous section, Zee has computed the Feynman diagram responsible for vacuum polarization, in which a photon converts briefly to a virtual electron-positron pair. In the first paragraph, he evaluates this expression, giving a concrete formula for the momentum-dependence of the electric charge, an important effect of quantum field theory. Next, he dismisses other possible diagrams that could affect the value of the electric charge. Most authors would give an explicit argument that these diagrams cancel, but for Zee it is more important to make the point that this result is expected and, from the right point of view, obvious. Finally, he discusses the implications for the relative size of the charges of the electron and the proton. If the magnitudes of charges are affected by interactions, and the proton has strong interactions but the electron does not, can it make sense that the charges of the proton and the electron are exactly equal and opposite? The answer is yes, and also that this was the real point of the whole derivation. The book takes on the full range of topics covered in typical graduate course in quantum field theory, and many additional topics: magnetic monopoles, solitons
NASA Astrophysics Data System (ADS)
Peskin, Michael E.
2011-04-01
Anthony Zee is not only a leading theoretical physicist but also an author of popular books on both physics and non-physics topics. I recommend especially `Swallowing Clouds', on Chinese cooking and its folklore. Thus, it is not surprising that his textbook has a unique flavor. Derivations end, not with `QED' but with exclamation points. At the end of one argument, we read `Vive Cauchy!', in another `the theorem practically exudes generality'. This is quantum field theory taught at the knee of an eccentric uncle; one who loves the grandeur of his subject, has a keen eye for a slick argument, and is eager to share his repertoire of anecdotes about Feynman, Fermi, and all of his heroes. A one-page section entitled `Electric Charge' illustrates the depth and tone of the book. In the previous section, Zee has computed the Feynman diagram responsible for vacuum polarization, in which a photon converts briefly to a virtual electron-positron pair. In the first paragraph, he evaluates this expression, giving a concrete formula for the momentum-dependence of the electric charge, an important effect of quantum field theory. Next, he dismisses other possible diagrams that could affect the value of the electric charge. Most authors would give an explicit argument that these diagrams cancel, but for Zee it is more important to make the point that this result is expected and, from the right point of view, obvious. Finally, he discusses the implications for the relative size of the charges of the electron and the proton. If the magnitudes of charges are affected by interactions, and the proton has strong interactions but the electron does not, can it make sense that the charges of the proton and the electron are exactly equal and opposite? The answer is yes, and also that this was the real point of the whole derivation. The book takes on the full range of topics covered in typical graduate course in quantum field theory, and many additional topics: magnetic monopoles, solitons