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1

Lagrangian Theory for the Second-Rank Tensor Field.

National Technical Information Service (NTIS)

The second-rank field is decomposed into its various subspaces under the Lorentz group and the appropriate projection operators are exhibited explicitly. The most general local, Hermitian, free-field Lagrangian which can be formed from this field is writt...

K. J. Barnes

1964-01-01

2

Generalization of the extended Lagrangian formalism on a field theory and applications

Formalism of extended Lagrangian represents a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field, and nonlinear sigma model.

Deriglazov, A. A.; Rizzuti, B. F. [Departamento de Matematica, ICE, Universidade Federal de Juiz de Fora, MG (Brazil) and Departamento de Fisica, ICE, Universidade Federal de Juiz de Fora, MG (Brazil)

2011-06-15

3

New parametrization for the Lagrangian density of relativistic mean field theory

A new parametrization for an effective nonlinear Lagrangian density of relativistic mean field (RMF) theory is proposed, which is able to provide a very good description not only for the properties of stable nuclei but also for those far from the valley of beta stability. In addition the recently measured superdeformed minimum in the 194Hg nucleus is reproduced with high

G. A. Lalazissis; J. Koenig; P. Ring

1997-01-01

4

We present a consistent Lagrangian quantum theory for one degree of freedom based on the Fréchet derivative. We consider a quantum mechanical system with one independent coordinate q and Lagrangian L(q,qdot) = a(q)qdot2 + b(q)qdot + c(q). In a consistent quantum theory, the canonical equal-time commutation relation (c.c.r.), [q,qdot] = i\\/2a(q) must be preserved in time; that is to say

F. J. Bloore; L. Routh; J. Underhill

1973-01-01

5

A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory

The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the former playing a role of a (typical) fibre of the letter one. Suitable sections of that bundle replace the ordinary state vectors and the operators on the system's Hilbert space are transformed into morphisms of the same bundle. In particular, the field operators are mapped into corresponding field morphisms.

Iliev, Bozhidar Z. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)

2011-04-07

6

n-symplectic algebra of observables in covariant Lagrangian field theory

NASA Astrophysics Data System (ADS)

n-symplectic geometry on the adapted frame bundle ?:L?E-->E of an n=(m+k)-dimensional fiber bundle ?:E-->M is used to set up an algebra of observables for covariant Lagrangian field theories. Using the principle bundle ?:L?E-->J1? we lift a Lagrangian L:J1?-->R to a Lagrangian L??*(L):L?E-->R, and then use L to define a ``modified n-symplectic potential'' ??L on L?E, the Cartan-Hamilton-Poincaré (CHP) Rn-valued 1-form. If the lifted Lagrangian is nonzero, then (L?E,d??L) is an n-symplectic manifold. To characterize the observables we define a lifted Legendre transformation ?L from L?E into LE. The image QL??L(L?E) is a submanifold of LE, and (QL,d(??|QL)) is shown to be an n-symplectic manifold. We prove the theorem that ??L=?L*(?|QL), and pull back the reduced canonical n-symplectic geometry on QL to L?E to define the algebras of observables on the n-symplectic manifold (L?E,d??L). To find the reduced n-symplectic algebra on QL we set up the equations of n-symplectic reduction, and apply the general theory to the model of a k-tuple of massless scalar fields on Minkowski space-time. The formalism set forth in this paper lays the ground work for a geometric quantization theory of fields.

Norris, L. K.

2001-10-01

7

A study on relativistic lagrangian field theories with non-topological soliton solutions

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.

Diaz-Alonso, J. [LUTH, Observatoire de Paris, CNRS, Universite Paris Diderot, 5 Place Jules Janssen, 92190 Meudon (France); Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)], E-mail: joaquin.diaz@obspm.fr; Rubiera-Garcia, D. [Departamento de Fisica, Universidad de Oviedo, Avda. Calvo Sotelo 18, E-33007 Oviedo, Asturias (Spain)

2009-04-15

8

A study on relativistic lagrangian field theories with non-topological soliton solutions

NASA Astrophysics Data System (ADS)

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call “admissible” models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.

Diaz-Alonso, J.; Rubiera-Garcia, D.

2009-04-01

9

Effective Lagrangians for scalar fields and finite size effects in field theory

NASA Astrophysics Data System (ADS)

We first discuss the approach of effective field theory in a d-dimensional Euclidean space. We consider a model with two interacting scalar fields (Lint(?1,J2)=(?2/2)(J1J2)2) with masses m1 and m2. Assuming m2>>m1 we show that there is a decoupling in the effective theory describing the dynamic of the light mass field. Furthermore, we consider the presence of two parallel hyperplanes which break translational symmetry, with a natural cutoff satisfying m2>>?>m1. Then imposing Dirichlet and also Neumann boundary conditions, we study the perturbative renormalization of the effective theory (?J4) in a region bounded by the two parallel hyperplanes in the one-loop approximation.

Caicedo, M. I.; Svaiter, N. F.

2004-01-01

10

Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians

NASA Astrophysics Data System (ADS)

This thesis includes several original results. All of them are already published or submitted for publication. I present here the short summary of main results: The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in AdS4 space is analyzed in details. One loop mass renormalization is studied on a simple example. The conformal invariant Lagrangian with the k-th power of Laplacian for the hierarchy of conformally coupled scalars with increasing scaling dimensions connected with the k-th Euler density is rederived using the Fefferman-Graham ambient space approach. The corresponding gauged ambient metric, Fefferman- Graham expansion and extended Penrose-Brown-Henneaux transformations are proposed and analyzed. Linearized gauge invariant interactions of scalar and general higher even spin fields in the AdSD space are obtained. A generalized Weyl transformation is proposed and the corresponding Weyl invariant action for cubic coupling of a scalar to a spin ell field is constructed. Using Noether's procedure several cubic interactions between different HS gauge fields are derived, including cubic selfinteraction of even spin gauge fields in a flat background. Then the main result - the complete off-shell gauge invariant Lagrangian for the trilinear interactions of Higher Spin Fields with arbitrary spins s1, s2, s3 in a flat background is presented. All possibilities with different numbers of derivatives are discussed. Restrictions on the number of derivatives are obtained. For any possible number of derivatives this interaction is uniquely fixed by gauge invariance up to partial integration and field redefinition. Finally an off-shell generating function for all cubic interactions of Higher Spin gauge fields is presented. It is written in a compact way, and turns out to have a remarkable structure.

Mkrtchyan, Karapet

2010-10-01

11

The Lagrangian theory of Staeckel Systems

NASA Astrophysics Data System (ADS)

A purely Lagrangian formulation and a direct proof of the separation of variables theorem is given for what is called Staeckel Systems in dynamics and celestial mechanics. The proof is essentially based on some properties of determinants and minors (given in Appendix A). In contrast with the standard literature on the subject, the use of the Hamiltonian, canonical transformations or the Hamilton-Jacobi equation is avoided by using instead a more elementary approach based on the Lagrangian. In Appendix B we use the Kepler Problem as an illustration of the Lagrangian theory of Staeckel Systems.

Broucke, R.

1981-10-01

12

Computation of Lagrangian Coherent Structures from their Variational Theory

NASA Astrophysics Data System (ADS)

We describe a computational algorithm for detecting hyperbolic Lagrangian Coherent Structures (LCS) from a recently developed variational theory [1]. In contrast to earlier approaches to LCS, our algorithm is based on exact mathematical theorems that render LCS as smooth parametrized curves, i.e., trajectories of an associated ordinary differential equation. The algorithm also filters out LCS candidates that are pure artifacts of high shear. We demonstrate the algorithm on two-dimensional flow models and on an experimentally measured turbulent velocity field.[4pt] [1] G. Haller, A variational theory of hyperbolic Lagrangian Coherent Structures, Physica D 240 (2011) 574-598

Farazmand, Mohammad; Mathur, Manikandan; Haller, George

2011-11-01

13

Excursion set theory for modified gravity: Eulerian versus Lagrangian environments

NASA Astrophysics Data System (ADS)

We have revisited the extended excursion set theory in modified gravity models, taking the chameleon model as an example. Instead of specifying their Lagrangian size, here we define the environments by the Eulerian size, chosen to be of the same order of the Compton length of the scalar field by physical arguments. We find that the Eulerian and Lagrangian environments have very different environmental density contrast probability distributions, the former being more likely to have high matter density, which in turn suppress the effect of the fifth force in matter clustering and halo formation. The use of Eulerian environments also evades the unphysical restriction of having an upper mass limit in the case of Lagrangian environments. Two methods of computing the unconditional mass functions, numerical integration and Monte Carlo simulation, are discussed and found to give consistent predictions.

Li, Baojiu; Lam, Tsz Yan

2012-09-01

14

Hamiltonian and Lagrangian theory of viscoelasticity

The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of\\u000a a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved\\u000a energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents\\u000a an elastic medium interacting with a continuum of oscillators.

A. Hanyga; M. Seredynska

2008-01-01

15

Reconstructing baryon oscillations: A Lagrangian theory perspective

Recently Eisenstein and collaborators introduced a method to 'reconstruct' the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

Padmanabhan, Nikhil [Physics Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (United States); White, Martin [Departments of Physics and Astronomy, 601 Campbell Hall, University of California, Berkeley, California 94720 (United States); Cohn, J. D. [Space Sciences Laboratory, 601 Campbell Hall, University of California, Berkeley, California, 94720 (United States)

2009-03-15

16

General transformation theory of Lagrangian mechanics and the Lagrange group

NASA Astrophysics Data System (ADS)

The general transformation theory of Lagrangian mechanics is revisited from a group-theoretic point of view. After considering the transformation of the Lagrangian function under local coordinate transformations in configuration spacetime, the general covariance of the formalism of Lagrange is discussed. Next, the group of Lagrange (for all n-dimensional Lagrangian systems) is introduced, and some important features of this group, as well as of its action on the set of Lagrangians, are briefly examined. Only finite local transformations of coordinates are considered here, and no variational transformation of the action is required in this study. Some miscellaneous examples of the formalism are included.

Aguirre, M.; Krause, J.

1991-04-01

17

The Newtonian limit of metric gravity theories with quadratic Lagrangians

NASA Astrophysics Data System (ADS)

The Newtonian limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of general relativity. We investigate the limit in the metric approach which, with respect to the Palatini formulation, has been much less studied in the recent literature, due to the higher order of the field equations. In addition, we refrain from exploiting the formal equivalence of higher-order theories considering the analogy with specific scalar-tensor theories, i.e. we work in the so-called Jordan frame in order to avoid possible misleading interpretations of the results. Explicit solutions are provided for several different types of Lagrangians containing powers of the Ricci scalar as well as combinations of the other curvature invariants. In particular, we develop the Green's function method for fourth-order theories in order to find out solutions. Finally, the consistency of the results with respect to general relativity is discussed.

Capozziello, S.; Stabile, A.

2009-04-01

18

Covariant Lagrangian Methods of Relativistic Plasma Theory

The relativistic electromagnetic projection operators discovered by Fradkin are used to obtain a covariant decomposition of the motion of a relativistic charged particle into parallel motion and perpendicular gyration. The Lagrangian Lie transform method of Littlejohn is used to achieve a transformation to guiding-center coordinates in which the rapid oscillatory motion is removed. The natural guiding-center Poisson bracket structure and

Bruce Michael Boghosian

1987-01-01

19

Topics in low-dimensional field theory

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.

Crescimanno, M.J.

1991-04-30

20

NASA Astrophysics Data System (ADS)

Some model quantum field theories of interest in elementary particle physics are studied. The first is a theory of a photon interacting with scalar, spinor and/or vector fields with arbitrary gauge-invariant interactions, in 2 + 1 dimensions. It is shown that to all orders in perturbation theory, all corrections to the topological mass term (beyond the known one-loop correction) vanish identically. The second model is explored for the possibility that non-topological solitons called "Q-balls" can exist in the chiral Lagrangian used to describe the eight light mesons. It was discovered that they could exist for reasonable sizes of the higher order terms in the chiral Lagrangian. They are approximately stable because they carry strangeness, hence the name "K-balls." The last model is a theory of fermions on the lattice in which exciting numerical results were obtained by Weingarten and Velikson. They seemed to be demonstrating a chirally invariant way of defining a single fermion species on the lattice. A major element of their approach was destroying the regularity of the lattice with a random external field. The external field also destroys hermiticity. It is shown that their numerical results cannot be understood by doing perturbation theory in the size of the fluctuations in the external field. The results are also re-examined in a framework which goes beyond perturbation theory by finding self-consistent equations for the fermion propagator. In this framework, the conclusions of the perturbation theory are confirmed.

Hill, Brian Russell

21

A new Hamiltonian formalism for singular Lagrangian theories

We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the case, when the Hessian is zero is done using the mixed (envelope\\/general) solutions of the multidimensional Clairaut equation. The corresponding system of equations of motion

Steven Duplij

2009-01-01

22

Optimizing higher-Order Lagrangian Perturbation Theory for CDM Models

NASA Astrophysics Data System (ADS)

We report on the performance of Lagrangian perturbation theory up to the second order for the standard cold dark matter (SCDM) and broken scale invariance (BSI) scenarios. We normalize both models to the COBE data, the BSI model serves as an example of models which fit the small-scale power of galaxy surveys. We optimize Lagrangian perturbation solutions by removing small-scale power from the initial data and compare the results with those of numerical simulations. We find an excellent performance of the optimized Lagrangian schemes down to scales around the correlation length or smaller, depending on the statistics used for the comparison. The optimization scheme can be expressed in a way which is independent of the type of fluctuation spectrum and of the size of the simulations.

Weiss, A. G.; Gottlober, S.; Buchert, T.

23

Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom

We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard R{sup 2}, (Ricci){sup 2} terms, and in the next order contain (Riemann){sup 3} as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (nonlocal) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the (Riemann){sup 3} term.

Krasnov, Kirill [School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)

2010-04-15

24

Fully Lagrangian Renormalized Approximation theory of fluid turbulence: Progress report

The purpose of this paper is to discuss our refinement and extension of the work of Y. Kaneda on a Lagrangian Renormalized Approximation (LRA) for homogeneous hydrodynamic turbulence. Kaneda's results are important to the development of a consistent theory of turbulence because the LRA theory successfully overcomes the failure of other turbulence theories (namely the Direct Interaction Approximation) to predict the Kolmogorov wavenumber spectrum. It is thought that this success is due to the use of a Lagrangian rather than Eulerian description of the fluid so that convection of the small eddies by the large ones is properly treated. However, some aspects of these results are puzzling and are considered here. For example, the form of the correlation function and the value of the Kolmogorov constant, K, depend on the choice of the form of the correlation function.

Frieman, E.A.; Hagan, W.K.

1988-01-01

25

The Lagrangian formalism in the radiative transfer theory.

NASA Astrophysics Data System (ADS)

The paper is devoted to the application of the variational approach to the radiative transfer problems in the one-dimensional case. To this end the results of the rigorous mathematical theory are used. It is shown that the conservation law due to the form-invariance of Lagrangian with respect to the axes translation transformation entails both the Ambartsumian's invariance principle (1960) and Rybicki's quadratic relations (1977).

Krikorian, R. A.; Nikoghossian, A. G.

1996-09-01

26

a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory

NASA Astrophysics Data System (ADS)

We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.

Gupta, Saurabh; Malik, R. P.

27

Chiral field theory of 0{sup -+} glueball

A chiral field theory of 0{sup -+} glueball is presented. The Lagrangian of this theory is constructed by adding a 0{sup -+} glueball field to a successful Lagrangian of the chiral field theory of pseudoscalar, vector, and axial-vector mesons. The couplings between the pseodoscalar glueball field and the mesons are revealed via a U(1) anomaly. Quantitative study of the physical processes of the 0{sup -+} glueball of m=1.405 GeV is presented. The theoretical predictions can be used to identify the 0{sup -+} glueball.

Li Bingan [Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506 (United States)

2010-06-01

28

Metafluid dynamics as a gauge field theory

In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently,

A. C. Rodrigues Mendes; W. Oliveira; C. Neves; F. I. Takakura

2001-01-01

29

Symmetries in k-Symplectic Field Theories

k-symplectic geometry provides the simplest geometric framework for describing certain class of first-order classical field theories. Using this description we analyze different kinds of symmetries for the Hamiltonian and Lagrangian formalisms of these field theories, including the study of conservation laws associated to them and stating Noether's theorem.

Roman-Roy, Narciso [Departamento de Matematica Aplicada IV. Edificio C-3, Campus Norte UPC, C/Jordi Girona 1.08034 Barcelona (Spain); Salgado, Modesto; Vilarino, Silvia [Departamento de Xeometria e Topoloxia, Facultade de Matematicas, Universidade de Santiago de Compostela. 15782 Santiago de Compostela (Spain)

2008-06-25

30

The motion of charged particles in external electromagnetic fields is reviewed with the purpose of determining the whole set of constants of motion. The Johnson-Lippmann results concerning the interaction with a constant magnetic field are taken as the starting point of the study. Our results are obtained through simple group-theoretical arguments based essentially on extended Lie algebras associated with the kinematical group of the (constant) electromagnetic field involved in the interaction. Nonrelativistic Schroedinger (or Pauli) and relativistic Dirac Hamiltonians are considered. The corresponding Lagrangian densities are then studied when the charged particles move in arbitrary electromagnetic fields. Through Noether's theorem, we get the constants of motion when coordinate and gauge transformations are combined. These results complete the U(1)-gauge theory and relate the works of Bacry, Combe, and Richard and of Jackiw and Manton when external gauge fields are considered. These developments enhance the minimal-coupling principle, the U(1)-gauge theory, and Noether's theorem.

Beckers, J.; Hussin, V.

1984-06-15

31

Quantum noncanonical field theory: Symmetries and interaction

The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincare invariance in an auxiliary spacetime is found in the Lagrangian version of the path integral formulation. This invariance is contrasted with the idea of doubly (or deformed) special relativity. This analysis is then used to go from the free theory of a complex field to an interacting field theory.

Carmona, J. M.; Cortes, J. L.; Indurain, J.; Mazon, D. [Departamento de Fisica Teorica, Universidad de Zaragoza, Zaragoza 50009 (Spain)

2009-11-15

32

Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field.

Texturing an animated fluid is a useful way to augment the visual complexity of pictures without increasing the simulation time. But texturing flowing fluids is a complex issue, as it creates conflicting requirements: we want to keep the key texture properties (features, spectrum) while advecting the texture with the underlying flow — which distorts it. In this paper, we present a new, Lagrangian, method for advecting textures: the advected texture is computed only locally and follows the velocity field at each pixel. The texture retains its local properties, including its Fourier spectrum, even though it is accurately advected. Due to its Lagrangian nature, our algorithm can perform on very large, potentially infinite scenes, with less than 10 ms per frame. Our experiments show that it is well suited for a wide range of input textures, including, but not limited to, noise textures. PMID:21149889

Yu, Qizhi; Neyret, Fabrice; Bruneton, Eric; Holzschuch, Nicolas

2010-12-01

33

Holography and defect conformal field theories

We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS5×S5 bisected by an AdS4×S2 ``brane,'' is dual to N=4 super Yang-Mills theory in R4 coupled to an R3 defect. We propose a complete Lagrangian for the field theory dual, a novel

Oliver Dewolfe; Daniel Z. Freedman; Hirosi Ooguri

2002-01-01

34

Effective field theories from QCD.

National Technical Information Service (NTIS)

We present a method for extracting effective Lagrangians from QCD. The resulting effective Lagrangians are based on exact rewrites of cut-off QCD in terms of these new collective field degrees of freedom. These cut-off Lagrangians are thus 'effective' in ...

R. Sollacher

1994-01-01

35

A Lagrangian theory of the classical spinning electron

NASA Astrophysics Data System (ADS)

A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler-Lagrange equations associated with this Lagrangian for space-time position x exp-alpha provide a generalization of the Lorentz force law. The remaining Euler-Lagrange equations lead directly to the (generalized) Frenkel (1926)-Thomas (1927)-BMT (1959) equations.

Nash, P. L.

1984-06-01

36

About non standard Lagrangians in cosmology

A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.

Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)

2012-08-17

37

Modelling non-linear evolution using Lagrangian perturbation theory re-expansions

NASA Astrophysics Data System (ADS)

We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory (LPT) plus two key theoretical extensions. One advance involves identifying and fixing a previously ignored gauge-like degree of freedom relating quantities calculated in LPT to those measured by a preferred Friedmann-Robertson-Walker observer. Handling this connection between calculational and observer frames is physically essential and ensures a momentum conserving description. The second extension is to systematically re-expand the equations of motion to increase LPT's radius of convergence to the maximum future time prior to orbit crossing. The paper implements a complete algorithm and performs extensive `proof of principle' tests of the new method, including direct comparison to known solutions, evaluation of conserved quantities and formal convergence studies. All are satisfactory. We show that convergence is exponential in grid size and Lagrangian order and polynomial in step size. There are three powerful advantages afforded by the new technique: (1) it employs a smooth representation of all fields, and the results are not limited by particle induced shot-noise errors, (2) it permits the numerical error to be controlled by changing Lagrangian order and/or number of steps allowing, in principle, arbitrarily small errors to be achieved prior to orbit crossing and (3) it handles generic cold initial data (any periodic density and velocity fields, including those with initial rotational components). Together, these properties make the new technique well suited to handle quasi-linear scales where analytic methods and/or numerical simulations fail to provide suitably accurate answers.

Nadkarni-Ghosh, Sharvari; Chernoff, David F.

2013-05-01

38

Metafluid Dynamics as a Gauge Field Theory

In this paper, the analog of Maxwell electromagnetism for hydrodynamic\\u000aturbulence, the metafluid dynamics, is extended in order to reformulate the\\u000ametafluid dynamics as a gauge field theory. That analogy opens up the\\u000apossibility to investigate this theory as a constrained system. Having this\\u000apossibility in mind, we propose a Lagrangian to describe this new theory of\\u000aturbulence and, subsequently,

A. C. R. Mendes; C. Neves; W. Oliveira; F. I. Takakura

2003-01-01

39

Finding Lagrangian Structures via the Application of Braid Theory.

National Technical Information Service (NTIS)

The ability to accurately identify regions of mixing in two dimensional systems has applications in ocean and geophysical systems, as well as granular flows. Over the last decade, much work has been put into finding coherent structures in the Lagrangian f...

M. R. Allshouse

2010-01-01

40

Lagrangian formulation of higher spin theories on AdS space

In this short note we present a Lagrangian formulation for free bosonic Higher Spin fields which belong to massless reducible representations of D-dimensional anti-de Sitter group using an ambient space formalism.

Fotopoulos, Angelos; Tsulaia, Mirian [Department of Physics, University of Crete, 710 03 Heraklion, Crete (Greece); Panigrahi, Kamal L. [Department of Physics, Indian Institute of Technology, Guwahati, 781 039 (India)

2006-10-15

41

NASA Astrophysics Data System (ADS)

For a given Lagrangian, in general singular, containing higher order time derivatives, a dynamically equivalent Lagrangian with only first order time derivatives is constructed. A Hamiltonian structure for this first order Lagrangian is then found with the use of the Dirac theory of constraints. However, in contrast with the usual Dirac procedure the method presented here starts with the Euler-Lagrange equations of motion. It is shown that in the case of a nonsingular higher order Lagrangian, the Ostrogradsky dynamics is derived this way. Further, it is shown that ambiguities characteristic of higher order Lagrangian systems do not appear when using this construction. Also, for a given system of ODE, an equivalent first order ODE system, suitable for the construction of a Bateman type Lagrangian is given. The Hamiltonian structure of this Lagrangian is then derived with the use of the Dirac theory of constraints. The uniqueness of the structure is proven and special properties of the construction are discussed. A Hamiltonian for the Bateman Lagrangian for a damped harmonic oscillator is obtained. The system is then quantized. The Hamiltonian operator, its eigenvalues and eigenfunctions are explicitly given. The long time behavior of some observables is discussed.

Hebda, Piotr Wiktor

42

Towards a field theory of F-theory

We make a proposal for a bosonic field theory in twelve dimensions that admits the bosonic sector of eleven-dimensional supergravity as a consistent truncation. It can also be consistently truncated to a ten-dimensional Lagrangian that contains all the BPS p-brane solitons of the type IIB theory. The mechanism allowing the consistent truncation in the latter case is unusual, in that

N. Khviengia; Z. Khviengia; H. Lü; C. N. Pope

1998-01-01

43

NASA Astrophysics Data System (ADS)

We construct a Lagrangian description of irreducible integer higher spin representations of the Poincaré-group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach. Starting with a description of bosonic mixed-symmetry higher spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincaré module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincaré-group representations) into a first-class constraint system. For this purpose, we find, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincaré-group representation. As examples of the general procedure, we formulate the method of Lagrangian construction for bosonic fields subject to arbitrary Young tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model of massless rank-4 tensor field with spin (2,1,1) and second stage reducible gauge symmetries.

Buchbinder, I. L.; Reshetnyak, A.

2012-09-01

44

Knot Invariants and New Quantum Field Theory

We propose a new gauge theory of quantum electrodynamics (QED) and quantum\\u000achromodynamics (QCD) from which we derive knot invariants such as the Jones\\u000apolynomial. Our approach is inspired by the work of Witten who derived knot\\u000ainvariants from quantum field theory based on the Chern-Simon Lagrangian. From\\u000aour approach we can derive new knot invariants which extend the Jones

Sze Kui Ng

2000-01-01

45

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability--Theory

NASA Astrophysics Data System (ADS)

Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.

Andreussi, T.; Morrison, P. J.; Pegoraro, F.

2013-09-01

46

Lagrangian Coherent Structures and the Kinematic Theory of Unsteady Separation

NASA Astrophysics Data System (ADS)

The problem of determining where unsteady fluid flow separates from a no-slip boundary is long-standing and challenging. Despite some landmark advances, a practical criterion remains elusive. Recent theoretical developments in Lagrangian Coherent Structures, however, have a suggested a new approach to the problem. We review these ideas, and present the results of a combined experimental and numerical study of unsteady flow separation for a canonical flow geometry. Experimentally-detected material spikes are directly compared to separation profiles predicted from numerical shear-stress and pressure data. For steady, periodic, quasi-periodic and random forcing, fixed separation is observed, and experimental observations and theoretical predictions are in close agreement. The transition from fixed to moving separation is also reported, and methods for dealing with this scenario are discussed. In collaboration with Matthew Weldon, Gustaff Jacobs, San Diego State University; and George Haller, Morgan Stanley.

Peacock, Thomas

2008-11-01

47

Lorentz-Poincaré type aspects of the matter Lagrangian in General Relativity Theory

NASA Astrophysics Data System (ADS)

It is well known that the solution to the Einstein Field Equation, g??, can be either interpreted as the metric tensor itself or the mere gravitational field, their geochronometric correspondence being assured by the Equivalence Principle (e.g. Brown 2005). Within the field interpretation, which allows emphasis on physical effects of gravitation on microphysical constituents of matter, we expose gravitational Lorentz-Poincaré type properties of the relativistic gravitational matter Lagrangian. The Weierstrass parametrization (Johns 2005) of the matter Lagrangian LM in the explicit Lorentz-Poincaré type gravitation model is shown to render it equal to the standard matter Lagrangian -which can be reduced to the proper time invariant (g??dx? / d?dx? / d?)1/2 for the geodesic motion (Stephani 2004)- in GRT. As such the GRT matter Lagrangian can be interpreted to result -following a Legendre transformation- from the energy of the matter fields obtained from Gravitationally Modified Lorentz Transformations (Broekaert 2005). The resultant correspondence between matter Lagrangians exposes explicitly the Lorentz-Poincaré type features such as (coordinate) spatially-variable speed of light, c(r) = c'?2, partial Machian mass induction m(r, ?) = m0'??-3 and gravitational affecting of space and time observations in local coordinates in GRT. These features are only apparent relative to the coordinative manifold, while locally and in physical coordinates the effects all vanish in concordance with the local Minkowski metric.

Broekaert, Jan B.

2007-04-01

48

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling (“BR scaling”) and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak.

Chaejun Song

2001-01-01

49

On exact tachyon potential in open string field theory

In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order in derivatives and modulo some class of field redefinitions) is given by L = e-T(partialT)2+(1+T)e-T. Upon obvious change of variables this leads to the potential energy -phi2log

Anton A. Gerasimov; Samson L. Shatashvili

2000-01-01

50

On background-independent open-string field theory

A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ``space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant

Edward Witten

1992-01-01

51

Chiral Effective Theory with a Scalar Field

We report on an extension of Chiral Perturbation Theory including a scalar, isosiglet field [1](henceforth refered as {chi}PT{sub S}). We work out the chiral Lagrangian up to next-to-leading order (NLO) including the new field and present the expressions for the pion mass and the pion decay constant computed in this new theory, which feature distincly new analytical structure on the quark mass. We compare the new expressions and the standard Chiral Perturbation Theory ones with lattice data, and provide the values for the low energy constants obtained.

Tarrus, Jaume [Departament d'Estructura i Constituents de la Materia and Institut de Ciencies del Cosmos, Universitat de Barcelona (Spain); Diagonal, 647, E-08028 Barcelona, Catalonia (Spain)

2011-05-23

52

An effective-Lagrangian approach to resummation in a hot scalar theory

NASA Astrophysics Data System (ADS)

A well known feature of thermal field theories is the breakdown of the standard perturbative expansion. This breakdown is due to the appearance of the Bose-Einstein distribution which is singular in the low-momentum limit. In this thesis it is argued that an effective-Lagrangian approach can be used to restore perturbative calculability. To illustrate this point, the induced thermal mass of a scalar theory is computed to both one and two-loop order. It is shown that the results can be largely determined without the explicit evaluation of Feynman graphs. This technique is then used to calculate the finite-temperature effective potential in a scalar model with spontaneous symmetry breaking. One finds that the resummed expression for the effective potential is not valid in the region of parameter space where evidence of a first-order phase transition is observed. Therefore, contrary to some of the literature, one cannot conclude that this model exhibits a first-order phase transition.

Marini, Alexander Lawrence

53

Generalized Lee-Wick formulation from higher derivative field theories

We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.

Cho, Inyong; Kwon, O-Kab [School of Liberal Arts, Seoul National University of Technology, Seoul 139-743 (Korea, Republic of); Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of)

2010-07-15

54

This is a brief review of vacuum string field theory, a new approach to open string field theory based on the stable vacuum of the tachyon. We discuss the sliver state explaining its role as a projector in the space of half-string functionals. We review the construction of D-brane solutions in vacuum string field theory, both in the algebraic approach

Leonardo Rastelli; Ashoke Sen; Barton Zwiebach

2001-01-01

55

Analogy between Landau theory of phase transitions and Lagrangian mechanics

NASA Astrophysics Data System (ADS)

It is shown that the definition of a stable point in Landau theory is different from that used in mechanics. The implications for numerical work on phase transitions for systems that have a Lifshitz invariant are discussed.

Ribeiro Filho, A.; Tilley, D. R.; Žekš, B.

1984-01-01

56

Extension of the chiral perturbation theory meson Lagrangian to order p6

NASA Astrophysics Data System (ADS)

We have constructed the most general chirally invariant Lagrangian scrL6 for the meson sector at order p6. The result provides an extension of the standard Gasser-Leutwyler Lagrangian scrL4 to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the construction was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The claim to have obtained the most general Lagrangian relies on this systematic construction and on the elimination of redundant quantities using relations of which we are aware, rather than on a general formal proof of either completeness or independence. The ``equation-of-motion'' terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating p6 contributions to simple processes.

Fearing, H. W.; Scherer, S.

1996-01-01

57

Extension of the chiral perturbation theory meson Lagrangian to order {ital p}{sup 6}

We have constructed the most general chirally invariant Lagrangian {ital scrL}{sub 6} for the meson sector at order {ital p}{sup 6}. The result provides an extension of the standard Gasser-Leutwyler Lagrangian {ital scrL}{sub 4} to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the construction was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The claim to have obtained the most general Lagrangian relies on this systematic construction and on the elimination of redundant quantities using relations of which we are aware, rather than on a general formal proof of either completeness or independence. The {open_quote}{open_quote}equation-of-motion{close_quote}{close_quote} terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating {ital p}{sup 6} contributions to simple processes. {copyright} {ital 1995 The American Physical Society.}

Fearing, H.W.; Scherer, S. [TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia (Canada) V6T 2A3

1996-01-01

58

NASA Astrophysics Data System (ADS)

String theory has emerged as the leading candidate for a unified field theory of all known forces. However, it is impossible to trust the various phenomenological predictions of superstring theory based on classical solutions alone. It appears that the crucial problem of the theory, breaking ten dimensional space-time down to four dimensions, must be solved nonperturbatively before we can extract reliable predictions. String field theory may be the only formalism in which we can resolve this decisive question. Only a rigorous calculation of the true vacuum of the theory will determine which of the many classical solutions the theory actually predicts. In this review article, we summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. We also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group we call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). Thus, the geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory.

Kaku, Michio

59

Weyl and conformal covariant field theories

Summary It is shown that, by imposing covariance with respect to the 11-parameter Weyl group, most of the known renormalizable field\\u000a theories, and only these, are obtained and that they admit, locally in the Minkowski spaceM\\u000a 3,1, a conformal group as a higher symmetry group. Globally conformal covariant Lagrangian field theories are first defined in\\u000a a pseudo-Euclidean spaceM\\u000a 4,2, where the

P. Budini; P. Furlan; R. Raczka

1979-01-01

60

Dual field theory of strong interactions

A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.

Akers, D.

1987-07-01

61

Optimizing higher order Lagrangian perturbation theory for standard CDM and BSI models

NASA Astrophysics Data System (ADS)

We investigate the performance of Lagrangian perturbation theory up to the second order for two scenarios of cosmological large-scale structure formation, standard cold dark matter (SCDM) and broken scale invariance (BSI). We study the latter model as a representative of COBE-normalized CDM models which fit the small-scale power of galaxy surveys. In this context, we optimize the performance of the Lagrangian perturbation schemes by smoothing the small-scale fluctuations in the initial data. The results of the Lagrangian mappings obtained are computed for a set of COBE-normalized SCDM and BSI initial data of different sizes and at different times. We compare these results with those obtained with a numerical particle mesh (PM) code. We find an excellent performance of the optimized Lagrangian schemes down to scales close to the correlation length. This is explained by the counterintuitive fact that non-linearities in the model can produce more small-scale power, if initially such power is removed. The optimization schemes can be expressed in a way that is independent of the type of fluctuation spectrum and the size of the simulations.

Weiss, Arno G.; Gottlober, Stefan; Buchert, Thomas

1996-02-01

62

NASA Astrophysics Data System (ADS)

Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as 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 even for nonlinear and non-Gaussian signal inference problems. IFT algorithms exploit spatial correlations of the signal fields and benefit from techniques developed to investigate quantum and statistical field theories, such as Feynman diagrams, re-normalisation calculations, and thermodynamic potentials. The theory can be used in many areas, and applications in cosmology and numerics are presented.

Enßlin, Torsten

2013-08-01

63

The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of intensive high-frequency electromagnetic radiation are obtained. In weak, low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the intensity of the electromagnetic field.

I.Y. Dodin; N.J. Fisch; G.M. Fraiman

2003-02-06

64

Two Lagrangian particle models, APOLLO and MILORD, were used to simulate the first ETEX experiment. The role played by wind field, mixing height h and horizontal diffusivity KH appeared to be the most important aspects to be studied. The sensitivity to the accuracy of the input advection field was studied through the application of APOLLO using different ECMWF data sets

F Desiato; D Anfossi; S Trini Castelli; E Ferrero; G Tinarelli

1998-01-01

65

On p-Adic Sector of Open Scalar Strings and Zeta Field Theory

We consider construction of Lagrangians which may be suitable for description of p-adic sector of an open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and they contain the Riemann zeta function with the d'Alembertian in its argument. However, investigation of the field theory with Riemann zeta function is interesting in itself as well. We present a brief review and some new results.

Dragovich, Branko [Institute of Physics, Pregrevica 118, Zemun, P.O. Box 57, 11001 Belgrade (Serbia)

2010-06-17

66

New N = 2 superconformal field theories from M\\/F-theory orbifolds

We consider M-theory on (T2 × R2)\\/Zn with M5-branes wrapped on R2 One can probe this background with M5-branes wrapped on T2. The theories on the probes provide many new examples of N = 2 field theories without Lagrangian description. All these theories have Coulomb branches, and we find the corresponding Seiberg-Witten curves. The exact solution is encoded in a

Sergei Gukov; Anton Kapustin

1999-01-01

67

Understanding conformal field theory through parafermions and Chern Simons theory

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.

Hotes, S.A.

1992-11-19

68

Energetic ions moving upstream from the Earth's bow shock frequently appear at the sunward Lagrangian (L1) point. The most common orientation of the interplanetary magnetic field (IMF) during these upstream events is near-radial from the sun (the nominal direction for connection to the magnetosphere). However, strong unidirectional beams of ions streaming away from Earth, consistent with good magnetic connection to

E. C. Roelof; C. W. Smith; N. F. Ness; R. M. Skoug; R. L. Tokar

2002-01-01

69

Lagrangian simulation of the unsteady near field dynamics of planar buoyant plumes

The unsteady dynamics of planar plumes is investigated numerically with particular emphasis on the pulsating instability characterizing the source (nozzle) near field. This instability manifests itself as the periodic shedding of vortical structures from the nozzle. The Lagrangian Transport Element Method is used to provide high resolution two-dimensional simulations of the unaveraged variable density flow. Comparison with experimental results verifies

M. C. Soteriou; Y. Dong; B. M. Cetegen

2002-01-01

70

Fourth-order perturbative equations in Lagrangian perturbation theory for a cosmological dust fluid

NASA Astrophysics Data System (ADS)

We have derived fourth-order perturbative equations in Lagrangian perturbation theory for a cosmological dust fluid. These equations are derived under the supposition of Newtonian cosmology in the Friedmann-Lemaître-Robertson-Walker Universe model. Even if we consider the longitudinal mode in the first-order perturbation, the transverse mode appears in the third-order perturbation. Furthermore, in this case, six longitudinal-mode equations and four transverse-mode equations appear in the fourth-order perturbation. The application of the fourth-order perturbation leads to a precise prediction of the large-scale structure.

Tatekawa, Takayuki

2013-01-01

71

Group field theories are higher dimensional generalizations of matrix models.\\u000aTheir Feynman graphs are fat and in addition to vertices, edges and faces, they\\u000aalso contain higher dimensional cells, called bubbles. In this paper, we\\u000apropose a new, fermionic Group Field Theory, posessing a color symmetry, and\\u000atake the first steps in a systematic study of the topological properties of

Razvan Gurau

2009-01-01

72

A new approach to conformal invariant field theories

Summary A new approach to conformal invariant field theories is presented. The physical idea is to introduce a fundamental scale of\\u000a hadron phenomena by means of a dilatation noninvariant vacuum state in the framework of a scale-invariant Lagrangian field\\u000a theory. A new unconventional feature is that this programme can only be carried out if the «vacuum» state is not translation\\u000a invariant.

S. Fubini

1976-01-01

73

ELKO SPINOR FIELDS: LAGRANGIANS FOR GRAVITY DERIVED FROM SUPERGRAVITY

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor\\u000afields) belong -- together with Majorana spinor fields -- to a wider class of\\u000aspinor fields, the so-called flagpole spinor fields, corresponding to the\\u000aclass-(5), according to Lounesto spinor field classification based on the\\u000arelations and values taken by their associated bilinear covariants. There\\u000aexists only six such disjoint classes: the

ROLDÃO DA ROCHA; J. M. HOFF DA SILVA

2009-01-01

74

NASA Astrophysics Data System (ADS)

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-02-01

75

Theory of massive and massless Yang-Mills fields

Introducing the Lagrangian multiplier field chi-->(x), a canonical formalism for the Yang-Mills fields f-->mu(x) with mass M>=0 is proposed within the framework of an indefinite-metric quantum field theory. The formalism for the massive f-->mu has a well-defined zero-mass limit, and the reduction of the physical components of f-->mu as M-->0 is embodied in an elegant way. Using the field equation

J. P. Hsu; E. C. Sudarshan

1974-01-01

76

A two-field modified Lagrangian formulation for robust simulations of extrinsic cohesive zone models

NASA Astrophysics Data System (ADS)

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.

Cazes, F.; Coret, M.; Combescure, A.

2013-06-01

77

Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian

Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to an elegant nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true, without having been demonstrated to be true. This paper reviews a variety of results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This body of work sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, as well as on other intriguing features such as the phase structure of QCD. In addition, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.

Kronfeld, Andreas S.; /Fermilab

2012-03-01

78

Twenty-First Century Lattice Gauge Theory: Results from the Quantum Chromodynamics Lagrangian

NASA Astrophysics Data System (ADS)

Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to a simple nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true without having been demonstrated to be true. This article reviews various results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This research sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, and other intriguing features such as the phase structure of QCD. Also, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.

Kronfeld, Andreas S.

2012-11-01

79

Effective field theory of cosmological perturbations

NASA Astrophysics Data System (ADS)

The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu–Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.

Piazza, Federico; Vernizzi, Filippo

2013-11-01

80

Superstring field theories are formulated in terms of light-cone-gauge superfields that are functionals of string coordinates x(sigma) and vartheta(sigma). The formalism used preserves only the manifest SU(4) symmetry that corresponds to rotations among six of the eight transverse directions. In type I theories, which have one ten-dimensional supersymmetry and describe both open and closed strings, there are five interaction terms

Michael B. Green; John H. Schwarz

1984-01-01

81

Energetic ions (>15 keV) moving upstream from the Earth's bow shock frequently appear at the sunward Lagrangian point (L1) ~1.5×106km upstream from Earth. The most common orientation of the interplanetary magnetic field (IMF) at L1 during these upstream events is near-radial from the Sun (the nominal direction for connection to the magnetosphere). However, strong unidirectional beams of ions streaming away

D. K. Haggerty; E. C. Roelof; C. W. Smith; N. F. Ness; R. L. Tokar; R. M. Skoug

2000-01-01

82

NASA Astrophysics Data System (ADS)

We advocate the use of Daubechies wavelets as a basis for treating a variety of problems in quantum field theory. This basis has both natural large-volume and short-distance cutoffs, has natural partitions of unity, and the basis functions are all related to the fixed point of a linear renormalization group equation.

Bulut, Fatih; Polyzou, W. N.

2013-06-01

83

Boundary superstring field theory

Using the Batalin–Vilkovisky formalism we provide a detailed analysis of the NS sector of boundary superstring field theory. We construct explicitly the relevant BV structure and derive the master action. Furthermore, we show that this action is exactly equal to the superdisk worldsheet partition function as was recently conjectured.

Vasilis Niarchos; Nikolaos Prezas

2001-01-01

84

Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids

A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.

Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory

2012-07-19

85

Matter power spectrum from a Lagrangian-space regularization of perturbation theory

NASA Astrophysics Data System (ADS)

We present a new approach to computing the matter density power spectrum, from large linear scales to small, highly nonlinear scales. Instead of explicitly computing a partial series of high-order diagrams, as in perturbative resummation schemes, we embed the standard perturbation theory within a realistic nonlinear Lagrangian-space ansatz. We also point out that an “adhesion-like” regularization of the shell-crossing regime is more realistic than a “Zel’dovich-like” behavior, where particles freely escape to infinity. This provides a “cosmic web” power spectrum with good small-scale properties that provide a good matching with a halo model on mildly nonlinear scales. We obtain a good agreement with numerical simulations on large scales, better than 3% for k?1hMpc-1, and on small scales, better than 10% for k?10hMpc-1, at z?0.35, which improves over previous methods.

Valageas, Patrick; Nishimichi, Takahiro; Taruya, Atsushi

2013-04-01

86

NASA Astrophysics Data System (ADS)

We construct a class of cubic gauge-invariant actions for superstring field theory, gauge fix one of them and show that it reproduces the known superstring S-matrix. In our construction boson string fields are taken in the 0 picture and fermion string fields in the -1/2 picture. For 0 picture the bosonic kinetic term requires an insertion carrying -2 units of picture number. We construct all possible picture-changing operators with the required properties. We use the simplest of these to construct the superstring action we choose to analyze here. In the gauge b1 + b-1 = 0, the conformal mappings needed to evaluate the tree diagrams are algebraic, and this enables a completely explicit derivation of the Koba-Nielsen amplitudes. In this gauge the action formally linearizes, a phenomenon familiar from other Chern-Simons type theories. Nontrivial scattering amplitudes are obtained by approaching this gauge as a limit.

Preitschopf, Christian R.; Thorn, Charles B.; Yost, Scott

1990-06-01

87

In this paper, we analyze two effects caused by the Lagrangian nature of turbulent transfer which are usually ignored in the theory of turbulent premixed combustion. These effects are (i) the nonequilibrium behavior of the turbulent diffusion coefficient, which is important for modeling the initial stage of combustion (for example, in the spark ignition engine), and (ii) the existence of

V. L. Zimont; G. Pagnini

2011-01-01

88

Field theory questions for string theory answers

We discuss the field theory of 3-brane probes in F-theory compactifications in two configurations, generalizing the work of Sen and of Banks, Douglas and Seiberg. One configuration involves several parallel 3-brane probes in F-theory compactified on T4\\/Z2, while the other invloves a compactification of F-theory on T6\\/Z2 × Z2 (which includes intersecting D4 singularities). In both cases string theory provides

Ofer Aharony; Jacob Sonnenschein; Stefan Theisen; Shimon Yankielowicz

1997-01-01

89

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to higher dimensional topological\\u000a spaces. The perturbative development of the usual GFT’s is rather involved combinatorially and plagued by topological singularities\\u000a (which we discuss in great detail in this paper), thus very difficult to control and unsatisfactory.\\u000a \\u000a \\u000a Both these problems simplify greatly for the “colored” GFT

Razvan Gurau

2011-01-01

90

NASA Astrophysics Data System (ADS)

We consider a flux formulation of Double Field Theory in which fluxes are dynamical and field-dependent. Gauge consistency imposes a set of quadratic constraints on the dynamical fluxes, which can be solved by truly double configurations. The constraints are related to generalized Bianchi Identities for (non-)geometric fluxes in the double space, sourced by (exotic) branes. Following previous constructions, we then obtain generalized connections, torsion and curvatures compatible with the consistency conditions. The strong constraint-violating terms needed to make contact with gauged supergravities containing duality orbits of non-geometric fluxes, systematically arise in this formulation.

Geissbühler, David; Marqués, Diego; Núñez, Carmen; Penas, Victor

2013-06-01

91

Effective Field Theories of Nuclear Structure

NASA Astrophysics Data System (ADS)

Traditional nuclear structure calculations have been pushed to new heights recently by exploiting new methods and increased computational power.(B. Pudliner et al)., Phys. Rev. Lett. 74, 4396 (1995); S.E. Koonin et al., nucl-th/9602006 (1996). Nevertheless, these developments have been made without direct input from quantum chromodynamics (QCD), the basic theory of strong interactions. Effective Field Theory provides a framework for connecting the energy scales and degrees of freedom appropriate for nuclear structure with those in the underlying QCD. Recent work shows how spontaneously broken chiral symmetry constrains the systematics of few-body nuclei.(See, for example, J.L. Friar, Few-Body Systems Suppl. 99), 1 (1996). Important ingredients are dimensional power counting and the assumption of naturalness,(A. Manohar and H. Georgi, Nucl. Phys. B234), 189 (1984). which allow estimates of the sizes of terms in effective lagrangians and imply the hierarchy of nuclear many-body forces. The delicacies of nuclear saturation introduce formidable obstacles to the systematic extension of effective chiral field theory to finite densities. For heavier nuclei, however, the successes of relativistic mean-field phenomenology can be understood in terms of nonrenormalizable effective field theories that are consistent with the symmetries of QCD. This framework provides new insight into issues of relativistic versus nonrelativistic formulations, nucleon compositeness, vacuum contributions, and extrapolations to high density.

Furnstahl, Richard

1996-10-01

92

Structure of Nuclei in a Relativistic Meson-Baryon Quantum Field Theory

Relativistic Hartree equations for spherical nuclei are derived from a relativistic nuclear quantum field theory using a coordinate-space Green's function approach. The renormalizable field theory lagrangian includes the interaction of nucleons with (sigma), (omega), (rho), and (pi) mesons and the photon. The Hartree equations represent the \\

Charles Joseph Horowitz

1982-01-01

93

National Technical Information Service (NTIS)

We have found al the Lagrange Lorentz-invariant field theory models in two-dimentional space-time for the complex scalar field with the quadratic in field gradients Lagrangian which posses an infinite set of local conserved currents that are polynomial in...

B. S. Getmanov

1980-01-01

94

Noncommutative Field Theories and (super)string Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV\\/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations

I. Ya. Aref'eva; D. M. Belov; A. A. Giryavets; A. S. Koshelev; P. B. Medvedev

2002-01-01

95

Reverse engineering quantum field theory

NASA Astrophysics Data System (ADS)

An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.

Oeckl, Robert

2012-12-01

96

Introduction to gauge field theory

This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications.

Bailin, D.; Love, A.

1986-01-01

97

Quadratic Lagrangians and horizons

It has been known for some time that the standard isotropic cosmological model with an {ital R}{sup 2} Lagrangian has horizon-breaking solutions in the {ital t}{r arrow}0 singularity limit. We search for horizonless power-law solutions in the vacuum Bianchi type-I and orthogonal type-V cosmological models. We find that type V with an {ital R}{sup 2} Lagrangian does contain such solutions. At first glance this would suggest that quadratic theories might provide an alternative resolution to the horizon problem. However, for both the horizonless isotropic and type-V solutions we show that the eigenvalues of the linear vector field near the stationary points in phase space have opposite signs, demonstrating that such solutions are not Lyapunov stable. The addition of free quantum fields may stabilize the solutions.

Rothman, T.; Anninos, P. (Department of Physics and Center for Relativity, The University of Texas at Austin, Austin, Texas (USA))

1991-11-15

98

Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation

NASA Astrophysics Data System (ADS)

We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in 1/c. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semirelativistic approximation to the full Dirac-Maxwell equations.

Dixit, Anant; Hinschberger, Yannick; Zamanian, Jens; Manfredi, Giovanni; Hervieux, Paul-Antoine

2013-09-01

99

NASA Astrophysics Data System (ADS)

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 2e bosonic field. In particular, the (1) mid-infrared band including the nonvanishing of the restricted f-sum rule in the Mott insulator, (2) the T2 contribution to the thermal conductivity, (3) pseudogap, (4) bifurcation of the electron spectrum below the chemical potential, as recently seen in angle-resolved photoemission, (5) insulating behavior away from half-filling, (6) high- and low-energy kinks in the electron dispersion, and (7) T-linear resistivity all derive from the charge 2e bosonic field. We also calculate the inverse dielectric function and show that it possesses a sharp quasiparticle peak and a broad particle-hole continuum. The sharp peak is mediated by a new charge e composite excitation formed from the binding of a charge 2e boson and a hole and represents a distinctly new prediction of this theory. It is this feature that is responsible for the dynamical part of the spectral weight transferred across the Mott gap. We propose that electron-energy loss spectroscopy at finite momentum and frequency can be used to probe the existence of such a sharp feature.

Choy, Ting-Pong

100

Supersymmetric field theories on three-manifolds

NASA Astrophysics Data System (ADS)

We construct supersymmetric field theories on Riemannian three-manifolds {M} , focusing on {N} = 2 theories with a U(1)R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet containing the R-current and the energy-momentum tensor. The field theory on {M} possesses a single supercharge if and only if {M} admits an almost contact metric structure that satisfies a certain integrability condition. This may lead to global restrictions on {M} , even though we can always construct one supercharge on any given patch. We also analyze the conditions for the presence of additional supercharges. In particular, two supercharges of opposite R-charge exist on every Seifert manifold. We present general supersymmetric Lagrangians on {M} and discuss their flat-space limit, which can be analyzed using the R-current supermultiplet. As an application, we show how the flat-space two-point function of the energy-momentum tensor in {N} = 2 superconformal theories can be calculated using localization on a squashed sphere.

Closset, Cyril; Dumitrescu, Thomas T.; Festuccia, Guido; Komargodski, Zohar

2013-05-01

101

NASA Astrophysics Data System (ADS)

Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated by chameleons therefore depends sensitively on their environment, which makes for a rich phenomenology. In this paper, we review two recent results on chameleon phenomenology. The first result a pair of no-go theorems limiting the cosmological impact of chameleons and their generalizations: (i) the range of the chameleon force at cosmological density today can be at most ?Mpc (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time. These theorems imply that chameleons have negligible effect on the linear growth of structure, and cannot account for the observed cosmic acceleration except as some form of dark energy. The second result pertains to the quantum stability of chameleon theories. We show how requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound of m < 0.0073(?/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 2 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.

Khoury, Justin

2013-11-01

102

Noncommutative Field Theories and (super)string Field Theories

NASA Astrophysics Data System (ADS)

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, "comma" and matrix representations of vertices.

Aref'eva, I. Ya.; Belov, D. M.; Giryavets, A. A.; Koshelev, A. S.; Medvedev, P. B.

2002-11-01

103

Topological field theory and physics

Topological Yang - Mills theory with the Belavin - Polyakov - Schwarz - Tyupkin SU(2) instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discussed. By embedding topological Yang - Mills theory

Damiano Anselmi

1997-01-01

104

Finite field theories and causality

A condensed introduction to the basic concepts of causal perturbation theory is given. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis by avoiding infinities from the outset. It goes back to a seminal work by Henri Epstein and

Andreas Aste

2008-01-01

105

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning\\u000anoncommutative geometry in general, as well as noncommutative field theories\\u000aand string field theories. We consider noncommutative quantum field theories\\u000aemphasizing an issue of their renormalizability and the UV\\/IR mixing. Sen's\\u000aconjectures on open string tachyon condensation and their application to the\\u000aD-brane physics have led to wide investigations

I. Ya. Aref'eva; D. M. Belov; A. A. Giryavets; A. S. Koshelev; P. B. Medvedev

2001-01-01

106

Transformation Properties of the Lagrangian and Eulerian Strain Tensors.

National Technical Information Service (NTIS)

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three- point tensor. The derivation explic...

T. B. Bahder

2002-01-01

107

On a Lagrangian formulation for a massive tensor field with spin (2,1,1) in Minkowski backgrounds

NASA Astrophysics Data System (ADS)

A Lagrangian for a new model of a massive rank 4 tensor field with a generalized spin (2,1,1) in Minkowski spacetime of d > 5 dimension is derived. Use is made of a dimensional reduction to a reducible gauge model of a massless tensor field of rank 4 with a generalized spin (2,1,1) in ( d+1)-dimensional Minkowski spacetime.

Reshetnyak, A. A.; Moshin, P. Yu.

2013-08-01

108

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field

NASA Astrophysics Data System (ADS)

We develop a relativistic variational model for a nematic liquid crystal interacting with an electromagnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the nonrelativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.

Obukhov, Yuri N.; Ramos, Tomás; Rubilar, Guillermo F.

2012-09-01

109

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field.

We develop a relativistic variational model for a nematic liquid crystal interacting with an electromagnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the nonrelativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium. PMID:23030929

Obukhov, Yuri N; Ramos, Tomás; Rubilar, Guillermo F

2012-09-17

110

Variational Methods for Field Theories

The thesis has four parts, dealing with four field theory models: 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;

Shahar Ben-Menahem

1982-01-01

111

NASA Astrophysics Data System (ADS)

In this paper, a new particle image velocimetry (PIV)-based measurement method is proposed to obtain the high-resolution tide-induced Lagrangian residual current field in the laboratory. A long gravity wave was generated to simulate the tide in a narrow tank full of water laden with PIV particles. Consecutive charge-coupled device (CCD) images were recorded with the studied layer illuminated with a laser beam. Two images separated by one tidal period were processed by applying the pattern-matching algorithm to get the horizontal tide-induced Lagrangian residual current field. The results coincide with sporadic results from the traditional surface-float tracing method, but with much higher spatial resolution and accuracy. Furthermore, it is found that the direct acquisition of the Lagrangian residual current may reduce the error at least by one order compared with those acquisition methods that require the detailed information of the tidal cycle.

Wang, Tao; Jiang, Wensheng; Chen, Xu; Feng, Shizuo

2013-09-01

112

Aspects of affine Toda field theory

This paper describes affine Toda field theory which is a theory of r scalar fields in two-dimensional Minkowski space-time, where r is the rank of a compact semi-simple Lie algebra g. The classical field theory is determined by the lagrangian density L = 1/2 {partial derivative}{sub {rho}}{phi}{sup a}{partial derivative}{sup {mu}}{phi}{sup a} {minus} V({phi}) where V({phi}) = m{sup 2}/{beta}{sup 2} {Sigma}{sub 0}{sup r}n{sub i}e{sup {beta}{alpha}{sub i} {center dot} {phi}}. m and {beta} are real, classically unimportant constants, {alpha}{sub i} i = 1, . . . ,r are the simple roots of the Lie algebra g, and {alpha}{sub 0} = {Sigma}{sub 1}{sup 4} n{alpha}{sub i} is a linear combination of the simple roots; it corresponds to the extra spot on an extended Dynkin diagram for g. A reasonable question to ask is whether the classical integrability survives into the quantum field theory and, if so, what is the spectrum and to what extent is it possible to calculate explicitly quantities of interest such as S-matrices and form factors. The recent discoveries leave no doubt that these relatively simple models have much structure and their study (even in the {beta}{sup 2} {gt} 0 regime) will be informative. In this short review, the ADE series of Lie algebras will be singled out for special attention.

Corrigan, E. (Durham Univ. (United Kingdom))

1992-06-01

113

Non-Abelian tensor gauge fields: Generalization of Yang–Mills theory

We suggest extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The invariant Lagrangian is expressed in terms of new higher rank field strength tensors. It does not contain higher derivatives of tensor

George Savvidy

2005-01-01

114

Free field theory as a string theory?

NASA Astrophysics Data System (ADS)

An approach to systematically implement open-closed string duality for free large N gauge theories is summarised. We show how the relevant closed string moduli space emerges from a reorganisation of the Feynman diagrams contributing to free field correlators. We also indicate why the resulting integrand on moduli space has the right features to be that of a string theory on AdS. To cite this article: R. Gopakumar, C. R. Physique 5 (2004).

Gopakumar, Rajesh

2004-11-01

115

A Renormalizable 4-Dimensional Tensor Field Theory

NASA Astrophysics Data System (ADS)

We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4 D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4 D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the {?^6} rather than of the {?^4} type, since two different {?^6}-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent {(int ?^2)^2} term, which can be interpreted as the generation of a scalar matter field out of pure gravity.

Geloun, Joseph Ben; Rivasseau, Vincent

2013-02-01

116

NASA Astrophysics Data System (ADS)

Starting with intersecting M2-branes in M-theory, the IIA supertube can be found by S compactification followed by a boost to the speed of light in the 11th dimension. A similar procedure applied to Donaldson Uhlenbeck Yau instantons on C, viewed as intersecting membranes of D=7 supersymmetric Yang Mills (SYM) theory, yields (for finite boost) a new set of 1/4 BPS equations for D=6 SYM-Higgs theory, and (for infinite boost) a generalization of the dyonic instanton equations of D=5 SYM-Higgs theory, solutions of which are interpreted as Yang Mills supertubes and realized as configurations of IIB string theory. To cite this article: P.K. Townsend, C. R. Physique 6 (2005).

Townsend, Paul K.

2005-03-01

117

Field beables for quantum field theory

The deBroglie-Bohm pilot-wave theory is an interpretation of quantum theory in which the observer plays no fundamental role. In a pilot-wave theory, quantum systems are not only described by the state vector, but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on

W. Struyve

118

Cyclic foam topological field theories

NASA Astrophysics Data System (ADS)

This paper proposes an axiomatic form for cyclic foam topological field theories, that is, topological field theories corresponding to string theories where particles are arbitrary graphs. World surfaces in this case are 2-manifolds with one-dimensional singularities. I prove that cyclic foam topological field theories are in one-to-one correspondence with graph-Cardy-Frobenius algebras that are families (A,B?,?) where A={As|s?S} are families of commutative associative Frobenius algebras, B?=?B? is an associative algebra of Frobenius type graduated by graphs, and ?={??s:As?End(B?)|s?S,???} is a family of special representations. Examples of cyclic foam topological field theories and graph-Cardy-Frobenius algebras are constructed.

Natanzon, Sergey M.

2010-06-01

119

We reveal nonmanifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian description of a six-dimensional free chiral field derived from the Bagger-Lambert-Gustavsson model in [P.-M. Ho and Y. Matsuo, J. High Energy Phys. 06 (2008) 105.] and make this formulation covariant with the use of a triplet of auxiliary scalar fields. We consider the coupling of this self-dual construction to gravity and its supersymmetrization. In the case of the nonlinear model of [P.-M. Ho, Y. Imamura, Y. Matsuo, and S. Shiba, J. High Energy Phys. 08 (2008) 014.] we solve the equations of motion of the gauge field, prove that its nonlinear field strength is self-dual and find a gauge-covariant form of the nonlinear action. Issues of the relation of this model to the known formulations of the M5-brane worldvolume theory are discussed.

Pasti, Paolo; Tonin, Mario [Dipartimento di Fisica 'Galileo Galilei', Universita degli Studi di Padova (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy); Samsonov, Igor [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk (Russian Federation); Sorokin, Dmitri [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via F. Marzolo 8, 35131 Padova (Italy)

2009-10-15

120

The effect of spatial and temporal resolutions and random errors on identification of Lagrangian coherent structures (LCSs) from Eulerian velocity fields is evaluated using two canonical flows: a two-dimensional vortex pair and a vortex ring formed by transient ejection of a jet from a tube. The flow field for the vortex pair case was steady and obtained analytically while the transient vortex ring flow was simulated using computational fluid dynamics. To evaluate resolution and random error effects, the flow fields were degraded by locally smoothing the flow and sampling it on a sparser grid to reduce spatial resolution, adding Gaussian distributed random noise to provide random errors, and/or subsampling the time series of vector fields to reduce the temporal resolution (the latter applying only for the vortex ring case). The degradation methods were meant to emulate distortions and errors introduced in common flow measurement methods such as digital particle image velocimetry. Comparing the LCS corresponding to the vortex boundary (separatrix) obtained from the degraded velocity fields with the true separatrix (obtained analytically for the vortex pair case or from high resolution, noise-free velocity fields for the vortex ring case) showed that noise levels as low as 5%-10% of the vortex velocity can cause the separatrix to significantly deviate from its true location in a random fashion, but the "mean" location still remained close to the true location. Temporal and spatial resolution degradations were found to primarily affect transient portions of the flow with strong spatial gradients. Significant deviations in the location of the separatrix were observed even for spatial resolutions as high as 2% of the jet diameter for the vortex ring case. PMID:20370296

Olcay, Ali B; Pottebaum, Tait S; Krueger, Paul S

2010-03-01

121

Statistical field theory of a nonadditive system

NASA Astrophysics Data System (ADS)

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.

Olemskoi, A. I.; Yushchenko, O. V.; Badalyan, A. Yu.

2013-03-01

122

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is

Edward Witten

1988-01-01

123

Generalized Noether theorems in canonical formalism for field theories and their applications

NASA Astrophysics Data System (ADS)

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.

Li, Zi-Ping

1993-01-01

124

NASA Astrophysics Data System (ADS)

In the ocean, geostrophic velocity fields inferred from sea surface height (SSH) are often used to assess mixing structures and other properties. If the ocean is assumed to be in geostrophic balance, then the velocity of the geostrophic currents can be calculated. Here we investigate the differences between geostrophic and non-geostrophic velocity fields and mixing using a Regional Ocean Modeling System (ROMS) model of an idealized Eastern boundary current. A geostrophic velocity field was calculated from the model sea surface height and compared with model output surface velocities using both Eulerian and Lagrangian methods. Simulated test particles in MATLAB were placed globally and near the coast in each vector field and their trajectories were calculated by using the Runge Kutta 4th order method. By binning the particles and looking at their densities, we were able to measure where the particles accumulate and relate this to the difference in the two velocity fields. To calculate the different ways the particles accumulated in both vector fields the mixing efficiency and index of aggregation were used. Areas where the divergence of the ROMS vector field was non-zero were looked at in comparison to the difference in the magnitudes of the two velocities. I hypothesized that the areas of high velocities correlated with the high SSH gradient and sea surface temperature gradient. When the magnitude of the Rossby number for the ROMS vector field is less than one it should correlate to smaller differences between the two vector fields. Another hypothesis was that when the magnitude of the sea surface temperature (SST) or SSH gradient was high, there would be lots of error. Eddies and other ocean phenomena were looked at to see how well the geostrophic velocities modeled them. Where particles accumulate should correlate to areas of high biological accumulation, especially in the case of coastally released particles. This leads to higher rates of foraging by predators. It is important to understand the difference in the two velocity fields because we might be underestimating the biological processes using geostrophic velocity fields.

Prakash, A.; Harrison, C. S.

2011-12-01

125

NASA Astrophysics Data System (ADS)

Halos are biased tracers of the dark matter distribution. It is often assumed that the initial patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in the dark matter density fluctuation field. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory) and provide an analytic model that provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it—this introduces k dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other type of nonlocality is due to the surrounding shear field; this affects the quadratic and higher-order bias factors and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in, e.g., analyses of higher-order clustering in Lagrangian or Eulerian space. Comparison of our predictions with measurements of the halo bispectrum in simulations is encouraging. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web—filaments, sheets and voids.

Sheth, Ravi K.; Chan, Kwan Chuen; Scoccimarro, Román

2013-04-01

126

Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect

We derive the lagrangian and transformation laws of the coupled Yang-Mills-matter-supergravity system for unextended n = 1 local supersymmetry. We study the super-Higgs effect and the normal Higgs effect of the Yang-Mills gauge group G. In the case of N chiral multiplets ``minimally'' coupled to supergravity, transforming according to some N-dimensional, generally reducible representation of G, we find a model-independent

E. Cremmer; Sergio Ferrara; L. Girardello; A. van Proeyen

1983-01-01

127

In this paper we present an efficient numerical scheme for the recently introduced Geodesic Active Fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, while the parametrization invariance allows working with images of non-flat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach: data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this work, we compare the Geodesic Active Fields method against the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow [1], MRF image registration [2], and landmark-enhanced large displacement optical flow [3]. Overall, we can show the advantages of the proposed FastGAF method. It compares strictly favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework. PMID:23529085

Zosso, D; Bresson, X; Thiran, J

2013-03-20

128

(Studies in quantum field theory)

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.

Not Available

1990-01-01

129

We shall discuss properties of alpha-decay chains of recently produced superheavy elements Z=115 and Z=113 using the Lagrangian model NL-SV1 with the vector self-coupling of omega meson in the framework of the relativistic mean-field theory. It is shown that due to the improved shell structure of this model Lagrangian, the experimentally observed alpha-decay energies and half-lives are reproduced well. Further

M. M. Sharma; A. R. Farhan; G. Muenzenberg

2004-01-01

130

Quantum field theory without divergences

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to unmeasurable (and hence unphysical) quantities. This is because no physical quantity can be measured in a point, but in a region, the size of which is constrained by the resolution of measuring equipment. The incorporation of the resolution into the definition of quantum fields {phi}(x){yields}{phi}{sup (A)}(x) and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean {phi}{sup 4}-field theory is taken as an example.

Altaisky, M. V. [Joint Institute for Nuclear Research, Dubna, 141980 (Russian Federation); and Space Research Institute RAS, Profsoyuznaya 84/32, Moscow, 117997 (Russian Federation)

2010-06-15

131

Toward Finite Quantum Field Theories

NASA Astrophysics Data System (ADS)

The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule ?s=0,1/2(-1)2 s+1(2 s+1) M {s/2}=0. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU (5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments.

Rajpoot, S.; Taylor, J. G.

1986-02-01

132

Field-theory methods in coagulation theory

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.

Lushnikov, A. A., E-mail: alex.lushnikov@mail.ru [Karpov Institute of Physical Chemistry (Russian Federation)

2011-08-15

133

Gravitational radiative corrections from effective field theory

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures 'post-Minkowskian' corrections to the multipole expansion due to nonlinear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from nonrelativistic binaries, including long distance effects up to 3 post-Newtonian (v{sup 6}) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

Goldberger, Walter D.; Ross, Andreas [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)

2010-06-15

134

A unitary and causal effective field theory

We report on a novel scheme based on the chiral Lagrangian. It is used to analyze pion-nucleon scattering, pion photoproduction, and nucleon Compton scattering. Subthreshold partial-wave amplitudes are calculated in chiral perturbation theory and analytically extrapolated with constraints imposed by electromagnetic-gauge invariance, causality and unitarity. Experimental quantities are reproduced up to energies {radical}(s){approx_equal}1300 MeV in terms of the parameters relevant at order Q{sup 3}.

Gasparyan, A. M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany); SSC RF ITEP, Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation); Lutz, M. F. M. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt (Germany)

2011-10-24

135

Field theories with « Superconductor » solutions

Summary The conditions for the existence of non-perturbative type « superconductor » solutions of field theories are examined. A non-covariant\\u000a canonical transformation method is used to find such solutions for a theory of a fermion interacting with a pseudoscalar boson.\\u000a A covariant renormalisable method using Feynman integrals is then given. A « superconductor » solution is found whenever in\\u000a the normal

J. Goldstone

1961-01-01

136

Introduction to string theory and conformal field theory

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.

Belavin, A. A., E-mail: belavin@itp.ac.ru; Tarnopolsky, G. M., E-mail: Hetzif@yandex.r [Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)

2010-05-15

137

Quantum Field Theory in Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34. Integrable models: dynamical mass generation; 35. A comparative study of dynamical mass generation in one and three dimensions; 36. One-dimensional spin liquids: spin ladder and spin S=1 Heisenberg chain; 37. Kondo chain; 38. Gauge fixing in non-Abelian theories: (1+1)-dimensional quantum chromodynamics; Select bibliography; Index.

Tsvelik, Alexei M.

2007-01-01

138

String theory inspired deformations of quantum field theories

In this dissertation, some extensions on field theories with deformations inspired by string theory are explored and their implications are investigated. These are: (i) noncommutative dipole field theory (DFT) and unitarity; (ii) three dimensional super Yang-Mills theory and mini-twistor string theory; (iii) massive super Yang-Mills theory and twistor string theory; and (iv) a deformation of twistor space and N =

Dah-Wei Chiou

2006-01-01

139

Bosonic colored group field theory

Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field\\u000a model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of Feynman\\u000a amplitudes in the “ultraspin” (large spin) limit. The results are generalized in any dimension. Finally, integrating out two\\u000a colors we write a

Joseph Ben Geloun; Jacques Magnen; Vincent Rivasseau

2010-01-01

140

National Technical Information Service (NTIS)

The one-loop amplitude of the Higgs-Higgs interaction is calculated in the fourth order of perturbation theory in the framework of the model with two Higgs doublets and an arbitrary number of fermions. The Lagrangian of this interaction is taken without a...

V. V. Dvoeglazov N. B. Skachkov

1991-01-01

141

AdS field theory from conformal field theory

NASA Astrophysics Data System (ADS)

We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative `1/ N ' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well- approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin fields in AdS by generalizing Weinberg's soft theorems to AdS/CFT. The AdS analog of Weinberg's argument constrains the interactions of conserved currents in CFTs, but there are potential loopholes that are unavailable to theories of massless higher spin particles in flat spacetime.

Fitzpatrick, A. Liam; Kaplan, Jared

2013-02-01

142

Planar limit of orientifold field theories and emergent center symmetry

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}xS{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. 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.

Armoni, Adi [Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP (United Kingdom); Shifman, Mikhail [William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 (United States); Uensal, Mithat [SLAC, Stanford University, Menlo Park, California 94025 (United States); Physics Department, Stanford University, Stanford, California, 94305 (United States)

2008-02-15

143

Bohmian mechanics and quantum field theory.

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end. PMID:15447078

Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino

2004-08-23

144

Supercomputers and quantum field theory

A review is given of why recent simulations of lattice gauge theories have resulted in substantial demands from particle theorists for supercomputer time. These calculations have yielded first principle results on non-perturbative aspects of the strong interactions. An algorithm for simulating dynamical quark fields is discussed. 14 refs.

Creutz, M.

1985-01-01

145

The analytic approach to the construction of the effective theory of strong interactions in the low-energy range is developed\\u000a and its application to pion-nucleon scattering is considered. A model-independent definition of renormalized coupling constants\\u000a of contact interactions of the effective chiral perturbation theory Lagrangian is proposed. With the help of the available\\u000a data of pion-nucleon phase-shift analysis the information on

A. N. Safronov

2009-01-01

146

Planar Limit of Orientifold Field Theories and Emergent Center Symmetry

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.

Armoni, Adi; Shifman, Mikhail; Unsal, Mithat

2007-12-05

147

Applications of effective Lagrangians

This thesis contains some applications of effective field theories in particle physics. The impact of a fourth generation of quarks on neutral kaon mixing is considered, and the results are extended to the mixing and CP violating phenomenology of neutral bottom meson systems. A phenomenological Lagrangian is constructed to describe radiative vector meson decays. The measured decay rates are reproduced, and one prediction is made. It is shown that the large-N approximation in the standard model cannot explain the {Delta}I = {1/2} rule for kaon nonleptonic decays, even when short distance effects such as Penguins are included. Finally, the contribution of small instantons to the axion potential is calculated. The induced potential can be a large if the QCD coupling is non-decreasing at high energies, and if a suppression by light quark masses can be avoided using loops of scalars.

Flynn, J.M.

1987-01-01

148

Symmetries in Three-Dimensional Superconformal Quantum Field Theories

NASA Astrophysics Data System (ADS)

Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ? 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].

Bashkirov, Denis

149

Effective-Lagrangian approach to the theory of pion photoproduction in the. Delta. (1232) region

We investigate theoretical uncertainties and model dependence in the extraction of the nucleon-{Delta}(1232) electromagnetic transition amplitudes from the multipole data base. Our starting point is an effective Lagrangian incorporating chiral symmetry, which includes, at the tree level, the pseudovector nucleon Born terms, leading {ital t}-channel vector-meson exchanges, and {ital s}- and {ital u}-channel {Delta} exchanges. We express the nucleon-{Delta} transition magnetic dipole ({ital M}1) and electric quadrupole ({ital E}2) amplitudes in terms of two independent gauge couplings at the {gamma}{ital N}{Delta} vertex, and fit these to various multipole data sets. We find a large sensitivity to the method used in unitarizing the amplitude, and extract the {ital E}2/{ital M}1 ratio (EMR) to be {ital negative}, with a magnitude of around 1.5%. The resonant amplitudes in this work are of interest to the test of topical hadron models inspired by QCD: the sign of the EMR, extracted by us, is in accord with that predicted by most realistic models, and its magnitude lies between the predictions of the quark shell model and the Skyrmion model. Finally, our work provides a phenomenologically satisfying unitary amplitude for pion photoproduction off nucleons, which can be used as a realistic starting point for theoretical studies of this process in complex nuclei.

Davidson, R.M.; Mukhopadhyay, N.C.; Wittman, R.S. (Physics Department, Rensselaer Polytechnic Institute, Troy, New York 12180-3590 (US))

1991-01-01

150

String field theory-inspired algebraic structures in gauge theories

We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab., 10 Hillhouse Ave., New Haven, Connecticut 06511 (United States)

2009-06-15

151

Studies on effective field theory in string theory

This thesis studies two aspects of effective field theories arising from string theory. In the first part, a new process of change of number of chiral fields in string theory compactification is proposed. It occurs quite generically, which is demonstrated in two cases: the perturbative heterotic string theory compactification on Calabi-Yau space, and type IIA orientifold construction with intersecting D6-branes.

Chengang Zhou

2003-01-01

152

Conformal techniques in string theory and string field theory

The application of some conformal and Riemann surface techniques to string theory and string field theory is described. First a brief review of Riemann surface techniques and of the Polyakov approach to string theory is presented. This is followed by a discussion of some features of string field theory and of its Feynman rules. Specifically, it is shown that the

Steven B. Giddings

1988-01-01

153

Conformal Techniques in String Theory and String Field Theory

The application of some conformal and Riemann surface techniques to string theory and string field theory is described. First a brief review of Riemann surface techniques and of the Polyakov approach to string theory is presented. This is followed by a discussion of some features of string field theory and of its Feynman rules. Specifically, it is shown that the

Steven B. Giddings

1987-01-01

154

NASA Astrophysics Data System (ADS)

This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Kármán wake of a cylindrical rod. The 3D velocity field measured at 5 kHz is used to evaluate the instantaneous planar pressure field by integration of the pressure gradient field. The experimental data are treated with a discretized model based on multiple velocity measurements. The time separation used to evaluate the Lagrangian derivative along a fluid parcel trajectory has to be taken into account to reduce precision error. By comparing Lagrangian and Eulerian approaches, the latter is restricted to shorter time separations and is found not applicable to evaluate pressure gradient field if a relative precision error lower than 10% is required. Finally, the pressure evaluated from tomographic velocity measurements is compared to that obtained from simulated planar ones to discuss the effect of 3D flow phenomena on the accuracy of the proposed technique.

Violato, Daniele; Moore, Peter; Scarano, Fulvio

2010-12-01

155

NASA Astrophysics Data System (ADS)

This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Kármán wake of a cylindrical rod. The 3D velocity field measured at 5 kHz is used to evaluate the instantaneous planar pressure field by integration of the pressure gradient field. The experimental data are treated with a discretized model based on multiple velocity measurements. The time separation used to evaluate the Lagrangian derivative along a fluid parcel trajectory has to be taken into account to reduce precision error. By comparing Lagrangian and Eulerian approaches, the latter is restricted to shorter time separations and is found not applicable to evaluate pressure gradient field if a relative precision error lower than 10% is required. Finally, the pressure evaluated from tomographic velocity measurements is compared to that obtained from simulated planar ones to discuss the effect of 3D flow phenomena on the accuracy of the proposed technique.

Violato, Daniele; Moore, Peter; Scarano, Fulvio

2011-04-01

156

Topics in string theory and quantum field theory

In this dissertation we study several topics in string theory and quantum field theory, which we collect into three main parts. The first part contains some studies in the context of twistor string theory. Witten proposed that the perturbative expansion of N = 4 super Yang-Mills theory has a dual formulation in terms of a topological string theory on the

Simone Giombi

2007-01-01

157

Diffeomorphisms in group field theories

We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.

Baratin, Aristide [Triangle de la Physique, CPHT Ecole Polytechnique, IPhT Saclay, LPT Orsay and Laboratoire de Physique Theorique, CNRS UMR 8627, Universite Paris XI, F-91405 Orsay Cedex (France); Girelli, Florian [School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Oriti, Daniele [Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, 14467 Golm (Germany)

2011-05-15

158

Variational methods for field theories

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.

Ben-Menahem, S.

1986-09-01

159

Chiral symmetry restoration in effective Lagrangian models

The restoration is studied of chiral symmetry in dense baryon matter using effective lagrangian models of QCD, in which baryons are described as topological solitons. Starting from the breaking of scale invariance and chiral symmetry in the QCD vacuum, the foundations are discussed of effective lagrangians and their relevance for applications to dense matter. Soliton models, such a the Skyrme model, show a phase transition at high densities, whose order parameter is the average scalar field. The properties are investigated of the two phases of the effective theory and show that the phase transition corresponds to the restoration of the chiral symmetry of QCD. It is argued that it should not be understood as deconfinement. The author then considers this phase transition in the context of the Cheshire Cat principle, which provides the link to the underlying quarks of QCD. An analogue of the Cheshire Cat property of this chiral bag model for baryons is found in solitons of effective lagrangians with a scalar glueball field. The Cheshire Cat interpretation of the results of effective lagrangians provides a consistent picture of chiral symmetry restoration at high densities. To verify this interpretation explicitly, the author finally generalizes the effective lagrangian approach to dense matter to a chiral bag model description with quark degrees of freedom.

Weiss, C.J.

1992-01-01

160

Effective field theories and inflation

We investigate the possible influence of very-high-energy physics on inflationary predictions, focusing on whether effective field theories can allow effects which are parametrically larger than order H2\\/M2, where M is the scale of heavy physics and H is the Hubble scale at horizon exit. By investigating supersymmetric hybrid inflation models, we show that decoupling does not preclude heavy physics having

C. P. Burgess; J. M. Cline; R. Holman

2003-01-01

161

Renormalized nonequilibrium quantum field theory: Scalar fields

We discuss the renormalization of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalized by counterterms determined in equilibrium. We emphasize the importance of the appropriate choice of initial conditions and go beyond the Gaussian initial density operator by defining self-consistent initial conditions. We study the corresponding time evolution and present a numerical example which supports the existence of a continuum limit for this type of initial conditions.

Borsanyi, Sz. [Department of Physics and Astronomy, University of Sussex, Brighton, East Sussex BN1 9QH (United Kingdom); Kavli Institute for Theoretical Physics, UCSB, Santa Barbara, California 93106 (United States); Reinosa, U. [Centre de Physique Theorique, Ecole Polytechnique, CNRS, 91128, Palaiseau (France)

2009-12-15

162

Symmetries and strings in field theory and gravity

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Z{sub p} gauge theories shows that they are associated with an emergent Z{sub p} 1-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear {sigma} models. It also allows us to expand on Polchinski's classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.

Banks, Tom [School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540 (United States); New High Energy Theory Center, Department of Physics, Rutgers University, Piscataway, New Jersey 08854 (United States); Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, California 95064 (United States); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540 (United States)

2011-04-15

163

Motion of small bodies in classical field theory

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.

Gralla, Samuel E. [Enrico Fermi Institute and Department of Physics University of Chicago 5640 S. Ellis Avenue, Chicago, Illinois 60637 (United States)

2010-04-15

164

The Quadratic Spinor Lagrangian, Axial Torsion Current and Generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to

R. Da Rocha; J. G. Pereira

2007-01-01

165

Gravitational Effects in Field Gravitation Theory.

National Technical Information Service (NTIS)

The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows ...

V. I. Denisov A. A. Logunov M. A. Mestvirishvili A. A. Vlasov

1979-01-01

166

Analytic Methods in Open String Field Theory

NASA Astrophysics Data System (ADS)

We review the basics of recent developments of analytic methods in open string field theory. We in particular explain Schnabl's analytic solution for tachyon condensation in detail, assuming only the basic knowledge on conformal field theory.

Okawa, Y.

2012-12-01

167

Effective field theory in nuclear physics

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.

Martin J. Savage

2000-12-12

168

From operator algebras to superconformal field theory

We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.

Kawahigashi, Yasuyuki [Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914 (Japan)

2010-01-15

169

From operator algebras to superconformal field theory

NASA Astrophysics Data System (ADS)

We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.

Kawashigashi, Yasuyuki

2010-01-01

170

Asymptotic Conservation Laws in Classical Field Theory

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. {copyright} {ital 1996 The American Physical Society.}

Anderson, I.M.; Torre, C.G. [Department of Mathematics, Utah State University, Logan, Utah 84322-3900 (United States)]|[Department of Physics, Utah State University, Logan, Utah 84322-4415 (United States)

1996-11-01

171

Quantum Field Theory in (0 + 1) Dimensions

ERIC Educational Resources Information Center

|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…

Boozer, A. D.

2007-01-01

172

Noncommutative Dipole Field Theories And Unitarity

We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.

Chiou, Dah-Wei; Ganor, Ori J.

2003-10-24

173

Topics in nonsupersymmetric field theory and string theory

In this two-part thesis, we study various non-supersymmetric aspects of field theory and string theory. In part I, we focus on N = 1 supersymmetric gauge theories. Nonperturbative effects in these theories can spontaneously break supersymmetry, a phenomenon known as dynamical supersymmetry breaking (DSB). Motivated by the search for simpler models of DSB, we explore the (phenomenologically viable) possibility that

David Shih

2006-01-01

174

Topics in effective field theory as applied to lattice QCD

NASA Astrophysics Data System (ADS)

This thesis focuses on understanding aspects of hadronic physics using numerical and analytic computations which comprise the research fields of Lattice QCD and Effective Field Theories. Lattice QCD is a numerical approximation to QCD that is computed within a finite spacetime volume, a finite lattice spacing, and unphysically large values of the quark mass used to limit computational run time. Because Lattice QCD calculations are implemented with these constraints, it becomes necessary to understand how these constraints influence the physics if we are to extract physical observables. This requires the use and matching of an effective field theory for mesons and baryons which are the fundamental degrees of freedom of the effective field theory Lagrangian. We consider pion and nucleon interactions in Chapter 3 when computational demands force the use of small, spacetime lattices, and extract the axial charge of the nucleon. In Chapters 4 and 5 we examine systems of up to twelve particles of single species, pions or kaons, and mixed species systems of pions and kaons. From these systems we learn about the scattering lengths and three-body forces of these particles. These multi-particle systems also allow one to understand the behavior of finite density systems on the lattice. Lastly in Chapter 6, we examine parton distributions of the pion for a nonzero change in the pion's momentum. These are known as generalized parton distributions and reveal information regarding the valence quarks within a particular hadron. Before the advent of QCD, however, these particles were also known as partons.

Smigielski, Brian

175

Progress in quantum field theory and string theory

We review some of the recent developments in Quantum Field Theory and String Theory. A thorough account of these subjects is virtually impossible, and I have therefore chosen a list of topics which should provide a reasonable cross section.

Alvarez-Gaume, L. (Theoretical Physics Division, CERN, CH - 1211 Geneva 23 (Switzerland))

1992-02-01

176

Large N field theories, string theory and gravity

We review the holographic correspondence between field theories and string\\/M theory, focusing on the relation between compactifications of string\\/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime

Ofer Aharony; Steven S. Gubser; Juan Maldacena; Hirosi Ooguri; Yaron Oz

2000-01-01

177

We argue that in a nonlinear gravity theory (the Lagrangian being an arbitrary function of the curvature scalar R), which according to well-known results is dynamically equivalent to a self-gravitating scalar field in general relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as the Einstein frame). Whenever such variables cannot

Guido Magnano; Leszek M. Sokolowski

1994-01-01

178

NASA Astrophysics Data System (ADS)

We develop an effective low-energy, long-wavelength theory of a bulk supersolid—a putative phase of matter with simultaneous crystallinity and Bose condensation. Using conservation laws and general symmetry arguments we derive an effective action that correctly describes the coupling between the Bose condensation and the elasticity of the solid. We use our effective action to calculate the correlation and response functions for the supersolid, and we show that the onset of supersolidity produces peaks in the response function, corresponding to propagating second sound modes in the solid. With a further study on the dissipative hydrodynamics of supersolids we show that the Brillouin peaks of the second sound modes in the response function actually originate from the splitting of the central Rayleigh peak corresponding to the defect diffusion mode under the supersolid transition. Light scattering may provide a direct measure of this splitting.

Yoo, C.-D.; Dorsey, Alan T.

2010-04-01

179

Gauge fields: introduction to quantum theory

A detailed exposition of quantum dynamics of gauge fields is presented. The classical dynamics of gauge fields and their geometric meaning are described first. Then a detailed exposition of path integral method in quantum theory is given. It is shown that this method allows consideration of all the specifics of gauge field theory. Quantization of the Yang-Mills field is discussed.

L. D. Faddeev; A. A. Slavnov

1980-01-01

180

Effective field theory calculation of second post-Newtonian binary dynamics

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.

Gilmore, James B.; Ross, Andreas [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States)

2008-12-15

181

Effective vector-field theory and long-wavelength universality of the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

We report on an effective vector-field theory of the fractional quantum Hall effect that takes into account projection to Landau levels. The effective theory refers to neither the composite-boson nor composite-fermion picture, but properly reproduces the results consistent with them, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states. In particular, the dual-field Lagrangian of Lee and Zhang is obtained, and an argument is given to verify the identification by Goldhaber and Jain of a composite fermion as a dressed electron. The generalization to double-layer systems is also remarked.

Shizuya, K.

2002-01-01

182

Proton drip-line nuclei in relativistic mean-field theory

The position of the two-proton drip line has been calculated for even-even nuclei with 10{le}Z{le}82 in the framework of the relativistic mean-field (RMF) theory. The current model uses the NL3 effective interaction in the mean-field Lagrangian and describes pairing correlations in the Bardeen-Cooper-Schrieffer (BCS) formalism. The predictions of the RMF theory are compared with those of the Hartree-Fock+BCS approach (with effective force Skyrme SIII) and the finite-range droplet model (FRDM) and with the available experimental information. {copyright} {ital 1998} {ital The American Physical Society}

Lalazissis, G.A.; Raman, S. [Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)

1998-09-01

183

Covariant field theory on frame bundles of fibered manifolds

NASA Astrophysics Data System (ADS)

We show that covariant field theory for sections of ? : E-->M lifts in a natural way to the bundle of vertically adapted linear frames L?E. Our analysis is based on the fact that L?E is a principal fiber bundle over the bundle of 1-jets J1?. On L?E the canonical soldering 1-forms play the role of the contact structure of J1?. A lifted Lagrangian L: L?E-->R is used to construct modified soldering 1-forms, which we refer to as the Cartan-Hamilton-Poincaré 1-forms. These 1-forms on L?E pass to the quotient to define the standard Cartan-Hamilton-Poincaré m-form on J1?. We derive generalized Hamilton-Jacobi and Hamilton equations on L?E, and show that the Hamilton-Jacobi and canonical equations of Carathéodory-Rund and de Donder-Weyl are obtained as special cases.

McLean, M.; Norris, L. K.

2000-10-01

184

Three-loop corrections in a covariant effective field theory

Chiral effective field theories have been used with success in the study of nuclear structure. It is of interest to systematically improve these energy functionals (particularly that of quantum hadrodynamics) through the inclusion of many-body correlations. One possible source of improvement is the loop expansion. Using the techniques of Infrared Regularization, the short-range, local dynamics at each order in the loops is absorbed into the parameterization of the underlying effective Lagrangian. The remaining nonlocal, exchange correlations must be calculated explicitly. Given that the interactions of quantum hadrodynamics are relatively soft, the loop expansion may be manageable or even perturbative in nuclear matter. This work investigates the role played by the three-loop contributions to the loop expansion for quantum hadrodynamics.

McIntire, Jeff [Department of Physics and Nuclear Theory Center, Indiana University, 727 E Third Street, Bloomington, IN 47405 (United States)], E-mail: oberonjwm@yahoo.com

2008-06-15

185

Perturbative nonequilibrium thermal field theory

NASA Astrophysics Data System (ADS)

We present a new perturbative formulation of nonequilibrium thermal field theory, based upon nonhomogeneous free propagators and time-dependent vertices. Our approach to nonequilibrium dynamics yields time-dependent diagrammatic perturbation series that are free of pinch singularities, without the need to resort to quasiparticle approximation or effective resummations of finite widths. In our formalism, the avoidance of pinch singularities is a consequence of the consistent inclusion of finite-time effects and the proper consideration of the time of observation. After arriving at a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory. The resulting equations do not rely upon a gradient expansion of Wigner transforms or involve any separation of time scales. To illustrate the key features of our formalism, we study out-of-equilibrium decay dynamics of unstable particles in a simple scalar model. In particular, we show how finite-time effects remove the pinch singularities and lead to violation of energy conservation at early times, giving rise to otherwise kinematically forbidden processes. The non-Markovian nature of the memory effects as predicted in our formalism is explicitly demonstrated.

Millington, Peter; Pilaftsis, Apostolos

2013-10-01

186

Non-Abelian gauge field theory in scale relativity

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.

Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry [Observatoire de Paris-Meudon, LUTH, CNRS, 5 Place Jules Janssen, 92195 Meudon Cedex (France)

2006-03-15

187

Quantum Field Theory in Condensed Matter Physics

This course in modern quantum field theory for condensed matter physics includes a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals. Alexei Tsvelik also covers Landau Fermi liquid theory and gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative

Alexei M. Tsvelik

2003-01-01

188

Some aspects of dualities in field theories and string theories

In this thesis we study examples of the dualities that have played very important roles in modern quantum field theories and string theories. In chapter 1, we start with an example of strong-weak coupling duality, the electromagnetic duality of d = 4 N = 4 super Yang-Mills (SYM4) theory. The low energy effective action of SYM4 is believed to have

2000-01-01

189

Toward a gauge field theory of gravity.

NASA Astrophysics Data System (ADS)

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.

Yilmaz, H.

190

Quantum equivalence of antisymmetric tensor field theories.

National Technical Information Service (NTIS)

We show in a very simple way that the quantum equivalence of massless antisymmetric second rank tensor field theories with massless scalar and gauge theories in four and five dimensions, respectively. The technique can be straightforwardly extended to hig...

V. O. Rivelles L. Sandoval

1990-01-01

191

Interaction theory of the electromagnetic field

An analysis of the field concept and its description in terms of field variables leads to the development of an Interaction Theory of the electromagnetic field with the following properties: (1) it is free of self-interaction terms; (2) the point charge model remains a viable conceptual element of the theory; (3) radiative reaction is fully accounted for within the framework

Solomon L. Schwebel

1972-01-01

192

Noncommutative Tachyons And String Field Theory

It has been shown recently that by turning on a large noncommutativity parameter, the description of tachyon condensation in string theory can be drastically simplified. We reconsider these issues from the standpoint of string field theory, showing that, from this point of view, the key fact is that in the limit of a large B-field, the string field algebra factors

Edward Witten

2000-01-01

193

Effective field theory of multi-field inflation a la Weinberg

NASA Astrophysics Data System (ADS)

We generalise Weinberg's effective field theory approach to multiple-field inflation. In addition to standard terms in the Lagrangian we consider terms containing up to the fourth derivative of the scalar fields and the metric. The results illustrate the possible shapes of the interactions which will yield non-Gaussianity. Generally we find that the speed of sound differs from, but is close to unity, however large non-Gaussianities are possible in the multi-field case. The non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude with the amount of the non-Gaussianity depending on the curvature of the classical field path in phase-space. We emphasize that in general the time derivative of adiabatic and entropy perturbations do not invariant due to the shift symmetry. However we find two specific combinations of them are invariant under such a symmetry and these combinations should be employed to construct an effective field theory of multi-field inflation.

Khosravi, Nima

2012-05-01

194

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed.

Wang Changyu [Qufu Normal University, Institute of Operations Research (China)], E-mail: wcy0537@126.com; Zhou Jinchuan [Beijing Jiaotong University, Department of Mathematics, School of Science (China)], E-mail: jinchuanzhou@yahoo.com.cn; Xu Xiuhua [Zibo Experimental High School (China)], E-mail: xxh123456@163.com

2009-06-15

195

The theory of the electromagnetic field

Aspects related to the concepts of charge and current are considered along with the effect of the electromagnetic field on general charge distributions, the electrical field produced by static charges, the magnetic induction field produced by steady currents, the electromagnetic field produced by time-dependent charge distributions, plane electromagnetic waves in vacuum, problems of potential theory, and time-dependent fields in the

D. M. Cook

1975-01-01

196

The antisymmetric tensor field in superstring theory

We discuss various aspects of the role of the antisymmetric tensor field in superstring theory, including the quantization law obeyed by its field strength and its role in topological defects and in vacuum configurations.

R. Rohm; E. Witten

1986-01-01

197

Finite temperature quantum field theory in curved spacetime

NASA Astrophysics Data System (ADS)

Several methods towards the formulation of theories of quantum fields in non equilibrium conditions are presented and applied to the studies of quantum thermal processes in the early Universe. The methods we introduce and problems studied include the zeta function method for static spacetimes, applied to the calculation of the finite temperature effective potential for a lambda phi (exp 4) field in static Taub spacetime. This result is useful for calculating the critical temperature for symmetry restoration of the scalar field. Another problem studied is an extension of the imaginary time formalism, coupled with a quasilocal expansion for slowly varying background fields to derive the one-loop finite temperature effective Lagrangian for lambda phi (exp 4) fields in curved spacetime. For spacetimes with small curvature, we use a Riemann normal coordinate for the metric and a derivative expansion for the background field. For homogeneous cosmologies we consider conformally related fields and the Robertson Walker universe as background to carry a thermal perturbation calculation. In addition, for a Bianchi type-1 universe, we use an expansion in orders of small anisotropy. Also discussed is a two particle irreducible effective action and 1/N approximation for O(N) lambda phi (exp 4) field for the study of symmetry behavior at finite temperature in curved spacetime. We find that for slowly varying fields the critical temperature is increased by an amount proportional to the second time derivative of the background field. For various spacetime dimensions and for static flat spacetime we calculate the finite temperature effective potential both at the one loop level and in a 1/N approximation. In both cases we find failure of dimensional reduction. As transition to quantum kinetic field theory and non equilibrium statistical field theory we calculate the Wigner function for a near thermal massive non conformal free scalar field in the Robertson Walker universe, and the one loop near thermal density matrix of a quasilocal system. To go beyond finite temperature we introduce the closed time patch effective action which is useful for treating non equilibrium quantum processes. As an example, we calculate the viscosity function for the scalar background field due to fermion pair production for the Yukawa interaction.

Stylianopoulos, Aris Michael

198

Geodesic Detection of Lagrangian Transport Barriers

NASA Astrophysics Data System (ADS)

Lagrangian transport barriers can be viewed as optimal material skeletons for observed tracer patterns. This idea leads to a variational problem whose solution forms the basis of the recent theory of geodesic transport barriers. This geodesic theory enables the computation of hyperbolic barriers (stable and and unstable manifolds), elliptic barriers (Lagrangian eddy boundaries), and parabolic barriers (Lagrangian jet cores) as parametrized curves in two-dimensional, finite-time velocity data sets. We show applications to numerical and observational geophysical flow data.

Haller, George

2013-04-01

199

Renormalization of Microphase Separation Field Theory

This work is concerned with the renormalization of the field theory describing microphase separation, in diblock copolymers or in chemically crosslinked two-component networks. The present theory differs from the usual phi4-theory only by the form of the propagator: 1\\/(k2 +m2 +(C)\\/(k2)), where \\

Mabrouk Benhamou

1993-01-01

200

Relativistic theory of infinite statistics fields

Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a relativistic quantum field theory which allows interactions involving infinite statistics particles. We also give some consistency analysis of this

Cao Chao; Chen Yixin; Li Jianlong

2009-01-01

201

Stochastic modeling of Lagrangian accelerations

NASA Astrophysics Data System (ADS)

It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.

Reynolds, Andy

2002-11-01

202

String Field Theory Around the Tachyon Vacuum

Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The

Leonardo Rastelli; Ashoke Sen; Barton Zwiebach

2000-01-01

203

Relativistic mean field theory in finite nuclei

Recent applications of relativistic mean field theory for finite nuclei are reviewed. We discuss the description of ground states of nuclei and their properties like nuclear radii as well as deformation parameters and their energy surfaces. In particular we concentrate on the description of exotic nuclei far from the line of beta-stability. A field theoretical theory for pairingcorrelations is presented

P. Ring

1996-01-01

204

Towards vacuum superstring field theory: The supersliver

We extend some aspects of vacuum string field theory to superstring field theory in Berkovits' formulation, and we study the star algebra in the fermionic matter sector. After clarifying the structure of the interaction vertex in the operator formalism of Gross and Jevicki, we provide an algebraic construction of the supersliver state in terms of infinite-dimensional matrices. This state is

Marcos Mariño; Ricardo Schiappa

2003-01-01

205

Monte Carlo approaches to effective field theories.

National Technical Information Service (NTIS)

In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nucl...

J. Carlson K. E. Schmidt

1991-01-01

206

A Theory of Mean Field Approximation

I present a theory of mean field approximation based on information ge- ometry. This theory includes in a consistent way the naive mean field approximation, as well as the TAP approach and the linear response the- orem in statistical physics, giving clear information-theoretic interpreta- tions to them.

Toshiyuki Tanaka

1998-01-01

207

Geometric engineering of quantum field theories

Using the recent advances in our understanding of non-perturbative aspects of type 11 strings we show how non-trivial exact results for N = 2 quantum field theories can be reduced to T-dualities of string theory. This is done by constructing a local geometric realization of quantum field theories together with a local application of mirror symmetry. This construction is not

Sheldon Katz; Albrecht Klemm; Cumrun Vafa

1997-01-01

208

Geometric Engineering of Quantum Field Theories

this paper is whether we can derive non-trivialfield theory results directly as a consequence of the recently acquired deeper understandingof string theory dynamics, rather than as a result of a consequence of a duality conjecture.If so we can claim to understand non-trivial results in field theory simply based on theexistence of string theory and its established properties! As we shall

Sheldon Katz; Albrecht Klemm; Cumrun Vafa

1996-01-01

209

Quantum field theory on noncommutative spaces

A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl–Wigner correspondence, noncommutative Feynman diagrams, UV\\/IR mixing, noncommutative Yang–Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study

Richard J. Szabo

2003-01-01

210

General Theory of Relativity of Einstein as Unified Field Theory

Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of physical interpretation of energy-momentum tensor components within GTR is required. A complete system of equations for numerical simulation of

Boris Mordvinov

1999-01-01

211

Space–time noncommutative field theories and unitarity

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space–time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there

Jaume Gomis; Thomas Mehen

2000-01-01

212

Green functions in stochastic field theory

NASA Astrophysics Data System (ADS)

Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.

Honkonen, Juha

2013-03-01

213

Lagrangian reduction and the double spherical pendulum

This paper studies the stability and bifurcations of the relative equilibrium of the double spherical pendulum, which has the circle as its symmetry group. The example as well as others with nonabelian symmetry groups, such as the rigid body, illustrate some useful general theory about Lagrangian reduction. In particular, we establish a satisfactory global theory of Lagrangian reduction that is

Jerrold E. Marsden; Juergen Scheurle

1993-01-01

214

Mass corrections in string theory and lattice field theory

Kaluza-Klein (KK) compactifications of higher-dimensional Yang-Mills theories contain a number of 4-dimensional scalars corresponding to the internal components of the gauge field. While at tree level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1 loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius R is much bigger than the scale of the UV completion (R>>{radical}({alpha}{sup '}), a), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in N=2, 4 super Yang-Mills is highly suppressed, even if the lattice regularization breaks all supersymmetries explicitly. This is due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.

Del Debbio, Luigi; Kerrane, Eoin; Russo, Rodolfo [SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Centre for Research in String Theory, Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)

2009-07-15

215

Giant Gravitons in Conformal Field Theory

Giant gravitons in AdS5 × S5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three

Vijay Balasubramanian; Micha Berkooz; Asad Naqvi; Matthew J. Strassler

2002-01-01

216

N=2 gauge theories and degenerate fields of Toda theory

We discuss the correspondence between degenerate fields of the W{sub N} algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W{sub N} algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W{sub N} generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.

Kanno, Shoichi; Matsuo, Yutaka; Shiba, Shotaro [Department of Physics, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tachikawa, Yuji [School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States)

2010-02-15

217

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of\\u000a augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve\\u000a the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle\\u000a points is that we do

Changyu Wang; Jinchuan Zhou; Xiuhua Xu

2009-01-01

218

Bosonization and effective vector-field theory of the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

The electromagnetic characteristics of the fractional quantum Hall states are studied by formulating an effective vector-field theory that takes into account projection to the exact Landau levels from the beginning. The effective theory is constructed, via bosonization, from the electromagnetic response of an incompressible and uniform state. It does not refer to either the composite-boson or composite-fermion picture, but properly reproduces the results of the standard bosonic and fermionic Chern-Simons approaches, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states and the associated quasiparticles. In particular, the dual-field Lagrangian of Lee and Zhang is obtained without invoking the composite-boson picture. An argument is also given to verify, within a vector-field version of the fermionic Chern-Simons theory, the identification by Goldhaber and Jain of a composite fermion as a dressed electron.

Shizuya, K.

2001-06-01

219

Radiation reaction and gravitational waves in the effective field theory approach

We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including radiation reaction forces and gravitational wave emission) and hereditary terms in the post-Newtonian approximation (including memory, tail and other causal, history-dependent integrals) within the EFT approach. We also provide a consistent formulation of the radiation sector in the equivalent effective field theory approach of Kol and Smolkin.

Galley, Chad R.; Tiglio, Manuel [Center for Scientific Computation and Mathematical Modeling and Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland, 20742 (United States)

2009-06-15

220

Weyl's Lagrangian in teleparallel form

The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.

Burnett, James; Vassiliev, Dmitri [Department of Mathematics and Institute of Origins, University College London, Gower Street, London WC1E 6BT (United Kingdom)

2009-10-15

221

The zero-bin and mode factorization in quantum field theory

We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In nonrelativistic field theories, the subtractions remove unphysical pinch singularities in box-type diagrams, and give a derivation of the known pullup mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formulas occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long-standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays.

Manohar, Aneesh V. [Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States); Stewart, Iain W. [Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2007-10-01

222

Mean-field theories of random advection

NASA Astrophysics Data System (ADS)

Two mean-field theories of random advection are formulated for the purpose of predicting the probability density function (PDF) of a randomly advected passive scalar, subject to an imposed mean scalar gradient. One theory is a generalization of the mean-field analysis used by Holzer and Pumir [Phys. Rev. E 47, 202 (1993)] to derive the phenomenological model of Pumir, Shraiman, and Siggia [Phys. Rev. Lett. 66, 2984 (1991)] governing PDF shape in the imposed-gradient configuration. The other theory involves a Langevin equation representing concentration time history within a fluid element. Predicted PDF shapes are compared to results of advection simulations by Holzer and Pumir. Both theories reproduce gross trends, but the Langevin theory provides the better representation of detailed features of the PDF's. An analogy is noted between the two theories and two widely used engineering models of turbulent mixing.

Kerstein, Alan R.; McMurtry, Patrick A.

1994-01-01

223

Consistent gravitationally coupled spin-2 field theory

NASA Astrophysics Data System (ADS)

Inspired by the translational gauge structure of teleparallel gravity, the theory for a fundamental massless spin-2 field is constructed. Accordingly, instead of being represented by a symmetric second-rank tensor, the fundamental spin-2 field is assumed to be represented by a spacetime (world) vector field assuming values in the Lie algebra of the translation group. The flat-space theory naturally emerges in the Fierz formalism and is found to be equivalent to the usual metric-based theory. However, the gravitationally coupled theory, with gravitation itself described by teleparallel gravity, is shown not to present the consistency problems of the spin-2 theory constructed on the basis of general relativity.

Arcos, H. I.; Gribl Lucas, Tiago; Pereira, J. G.

2010-07-01

224

Theory of lanthanide crystal fields

Recent progress in understanding the origin of the lanthanide crystal field is summarized. The basic assumption of the crystal field parametrization is shown to be that the crystalline environment can be represented as a one-electron potential, and the consequences of removing this assumption are traced. It is further shown that overlap and covalency make the dominant contributions to the observed

D. J. Newman

1971-01-01

225

Effective Procedures in Field Theory

Van der Waerden (1930 a, pp. 128-131) has discussed the problem of carrying out certain field theoretical procedures effectively, i.e. in a finite number of steps. He defined an 'explicitly given' field as one whose elements are uniquely represented by distinguishable symbols with which one can perform the operations of addition, multiplication, subtraction and division in a finite number of

A. Frohlich; J. C. Shepherdson

1956-01-01

226

Theory of force-free electromagnetic fields. I. General theory

A general method to deal with the (relativistic) force-free electromagnetic field is developed. We formulate the theory without assuming symmetry of the electromagnetic field configuration. Thus we can apply it to any object where the force-free approximation is justified, e.g., the pulsar magnetosphere, the black-hole magnetosphere, and the magnetosphere around the accretion disk. We describe the force-free electromagnetic field by

Toshio Uchida

1997-01-01

227

Lectures on interacting string field theory

We give a detailed review of the current formulations of interacting string field theory. The historical development of the subject is taken beginning with the old dual resonance model theory. The light cone approach is reviewed in some detail with emphasis on conformal mapping techniques. Witten's covariant approach is presented. The main body of the lectures concentrates on developing the operator formulation of Witten's theory. 38 refs., 22 figs., 5 tabs.

Jevicki, A.

1986-09-01

228

Effective Field Theory in Condensed Matter Physics

Some personal reminiscences are followed by a brief illustration of how effective field theories are used in condensed matter physics. Examples include Landau's Fermi liquid, sigma models with topological terms, Dirac fermions and the Gross Neveu model.

R. Shankar

1997-01-01

229

Klein Topological Field Theories from Group Representations

NASA Astrophysics Data System (ADS)

We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.

Loktev, Sergey A.; Natanzon, Sergey M.

2011-07-01

230

Mean Field Methods in Lattice Gauge Theories.

National Technical Information Service (NTIS)

Mean field theory for lattice gauge theory is formulated as a saddle point expansion. One-loop corrections are evaluated for Z(2), SO(3) and mixed SU(2)-SO(3). Excellent agreement with Monte Carlo data is obtained. (Atomindex citation 13:687689)

B. Lautrup

1982-01-01

231

A New Approach to Superstring Field Theory

I review the construction of an action for open superstring field theory\\u000awhich does not suffer from the contact term problems of other approaches. I\\u000aalso discuss a possible generalization of this action for closed superstring\\u000afield theory.

Nathan Berkovits

2000-01-01

232

Tachyon vacuum in cubic superstring field theory

In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in

Theodore Erler

2008-01-01

233

Field-Theory Amplitudes as Resurgent Functions

A series of informal seminars at graduate-student level on the subject of coupling dependence in quantum field theory, with an elementary introduction to the notion of resurgent function that forms the appropriate framework for the coupling dependence of strictly renormalizable theories. While most of the discussion is pedagogical, there are also a few things for the expert: we demonstrate, by

M. Stingl

2002-01-01

234

Pion masses in quasiconformal gauge field theories

We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.

Dietrich, Dennis D.; Jaervinen, Matti [Center for High Energy Physics, University of Southern Denmark, Odense (Denmark)

2009-03-01

235

Large q expansions for q-state gauge-matter Potts models in lagrangian form

We consider the lagrangian form of a q-state generalization of Ising gauge theories with matter fields in d = 3 and 4 dimensions. The theory is exactly soluble in the limit q --> ? and corrections are easily calculable in power series in 1\\/q1\\/d. Extrapolating the series for the free energies and latent heats by the method of Padé approximants,

Paul Ginsparg; Yadin Y. Goldschmidt; Jean-Bernard Zuber

1980-01-01

236

On field theory thermalization from gravitational collapse

NASA Astrophysics Data System (ADS)

Motivated by its field theory interpretation, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. After demonstrating the accuracy of the numerical algorithm for the questions we are interested in, we investigate various aspects of the apparent horizon formation. In particular, we study the time and radius of the apparent horizon formed as functions of the initial Gaussian profile for the scalar field. We comment on several aspects of the dual field theory picture.

Garfinkle, David; Pando Zayas, Leopoldo A.; Reichmann, Dori

2012-02-01

237

Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields

NASA Astrophysics Data System (ADS)

Large-eddy simulation (LES) of two-phase turbulent flows exhibits quantitative differences in particle statistics if compared to direct numerical simulation (DNS) which, in the context of the present study, is considered the exact reference case. Differences are primarily due to filtering, a fundamental intrinsic feature of LES. Filtering the fluid velocity field yields approximate computation of the forces acting on particles and, in turn, trajectories that are inaccurate when compared to those of DNS. In this paper, we focus precisely on the filtering error for which we quantify a lower bound. To this aim, we use a DNS database of inertial particle dispersion in turbulent channel flow and we perform a priori tests in which the error purely due to filtering is singled out removing error accumulation effects, which would otherwise lead to progressive divergence between DNS and LES particle trajectories. By applying filters of different type and width at varying particle inertia, we characterize the statistical properties of the filtering error as a function of the wall distance. Results show that filtering error is stochastic and has a non-Gaussian distribution. In addition, the distribution of the filtering error depends strongly on the wall-normal coordinate being maximum in the buffer region. Our findings provide insight on the effect of sub-grid scale velocity field on the force driving the particles, and establish the requirements that any closure model aimed at recovering sub-grid scale effects on the dynamics of inertial particles must satisfy.

Bianco, F.; Chibbaro, S.; Marchioli, C.; Salvetti, M. V.; Soldati, A.

2012-04-01

238

Nonlinear field theories during homogeneous spatial dilation

NASA Astrophysics Data System (ADS)

The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the properties of nonlinear field theories embedded in expanding Euclidean Friedmann-Lemaître-Robertson-Walker metrics in the context of cosmology, as well as different systems in the disciplines of statistical mechanics and condensed matter physics. Field theories are characterized by the speed at which they propagate correlations within themselves. We show that for linear field theories correlations stop propagating if and only if the speed at which the space dilates is higher than the speed at which correlations propagate. The situation is in general different for nonlinear field theories. In this case correlations might stop propagating even if the velocity at which space dilates is lower than the velocity at which correlations propagate. In particular, these results imply that it is not possible to characterize the dynamics of a nonlinear field theory during homogeneous spatial dilation a priori. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang equation.

Escudero, Carlos

2013-09-01

239

The quadratic spinor Lagrangian, axial torsion current, and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst\\u000aactions can be derived from the Quadratic Spinor Lagrangian (QSL), when the\\u000athree classes of Dirac spinor fields, under Lounesto spinor field\\u000aclassification, are considered. To each one of these classes, there corresponds\\u000aa unique kind of action for a covariant gravity theory. In other words, it is\\u000ashown to

Roldao da Rocha; J. G. Pereira

2007-01-01

240

World sheet commuting ?? conformal field theory and nonrelativistic string theories

NASA Astrophysics Data System (ADS)

We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri [J. Math. Phys. (N.Y.)JMAPAQ0022-2488 42, 3127 (2001)10.1063/1.1372697] and Danielsson et al. [J. High Energy Phys.JHEPFG1029-8479 10 (2000) 02010.1088/1126-6708/2000/10/020; J. High Energy Phys.JHEPFG1029-8479 03 (2001) 041.10.1088/1126-6708/2001/03/041]. Our theory is much simpler than their theory and does not assume a compact coordinate. This nonrelativistic string theory has a bosonic matter ?? conformal field theory with the conformal weight of ? as 1. It is natural to identify time as a linear combination of ? and ?¯ through an explicit realization of the Galilean boost symmetry. The angle between ? and ?¯ parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a nonrelativistic dispersion relation without a nontrivial topology in the nonrelativistic setup, which is one of the major differences from the previous works of Gomis and Ooguri and of Danielsson and co-workers. This simple theory is the nonrelativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the ?? conformal field theory. We also mention supersymmetric generalizations of these theories.

Kim, Bom Soo

2007-11-01

241

Field theory of fluctuations in glasses.

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments, we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be described through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations. PMID:21947902

Franz, S; Parisi, G; Ricci-Tersenghi, F; Rizzo, T

2011-09-26

242

Quantization of classical lagrangian mechanics

NASA Astrophysics Data System (ADS)

The equations of motion of a massive rigid body in the Lagrange—Poisson case (when one point of the body is fixed) are expressed in Hamiltonian form, making it possible to describe the Lagrangian rigid body in terms of classical mechanics. Using Berezin's quantization algorithm, it is possible to associate the Lagrangian classical mechanics with a quantum system, namely, a system of two-level particles interacting with a resonant field.

Bogdanov, E. I.

1992-06-01

243

Quantum algorithms for quantum field theories.

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 (?(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

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

244

2T physics field theory and supersymmetry

NASA Astrophysics Data System (ADS)

This thesis is a summary of the author's research work in 2T Physics during his PhD study in University of Southern California. After a brief introduction of the worldline theory of 2T spinless particle in chapter 1, transition from 2T-physics at the worldline level to the field theory level is made by using BRST quantization in chapter 2. A simpler way to generalize the theory to include spinning particles is briefly discussed too. In chapter 3, we will use the aformentioned 2T Physics Field Theory principle to establish supersymmetric field theories in 4+2 dimension. The theoretical and phenomenological impacts are also discussed in this chapter. In chapter 4, we will proceed to construct extended supersymmetric theories. In chapter 5, we will worked out a 10+2 dimensional Super YM theory which reduces to N=4 Super YM in 4+2 dimension upon dimensional reduction and can be gauge fixed into ordinary N=1 Super YM in 9+1 dimension. This will serve as an intermediate step toward the construction of 11+2 dimensional M theory in 2T language. And in the last chapter, we will outline the current status of 2T-Physics and give some comments for future directions.

Kuo, Yueh-Cheng

245

Daughters and Weinberg Field Theory.

National Technical Information Service (NTIS)

A recurrence relation is obtained for the Feynman amplitude for the scattering of four spinless particles due to the exchange of a particle with spin J, described by a (J, 0) field of Weinberg. It is shown that lower-spin contributions still occur in the ...

J. D. Jenkins

1969-01-01

246

Mean Field Theory for Collective Motion of Quantum Meson Fields

Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schrödinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the variational wavefunctional can be rewritten in a compact form similar to the Hartree-Bogoliubov equations in quantum many-body theory and this result is used

Yasuhiko Tsue; Dominique Vautherin; Tetsuo Matsui

1999-01-01

247

Field Redefinition and Renormalizability in Scalar Field Theories

NASA Astrophysics Data System (ADS)

We have addressed the issue of field redefinition in connection with renormalizability. Our study is restricted to theories of interacting scalar fields. We have, in particular, shown that if a theory is renormalizable in the usual power-counting sense then it remains renormalizable in the same sense after a change of variables. This is due to the use of the powerful method of the background field expansion. In the case of a single complex scalar field, it turns out that the determination of the counterterms is much simpler when polar coordinates are used. We illustrate this by carrying out a one-loop calculation in the latter case.

Mohammedi, N.

2013-10-01

248

Session 5: Component Applications of Field Theory

Field theory is continually being applied to useful component-oriented structures. The use of planar transmission line technology and miniaturized packaging demands an ever-increasing need for field solutions to produce scattering parameters, coupling coefficients, impedance parameters, radiation, etc. at the component-transmission line interface. This session on \\

E. J. Denlinger

1984-01-01

249

Mean field theory for optimal power flow

We present a method based on mean field theory to cope with the mixed nonlinear integer programming, especially with optimal power flow problems involving both continuous and discrete variables, in a more exact manner. That is, we first formulate OPF as a mixed integer programming, and then derive its mean field equations as well as the annealing algorithm, by taking

Luonan Chen; Hideki Suzuki; Kazuo Katou

1997-01-01

250

Gravity Field and Electromagnetic Field-Finite Geometrical Field Theory of Matter Motion Part Two

Gravity field theory and electromagnetic field theory are well established and confirmed by experiments. The Schwarzschild metric and Kerr Metric of Einstein field equation shows that the spatial differential of time gauge is the gravity field. For pure time displacement field, when its spatial differentials are commutative, conservative fields can be established. When its spatial differentials are non-commutative, Maxwell electromagnetic

Xiao Jianhua

2005-01-01

251

Field theory based covariant models

Various relativistic schemes based on effective field theoretical models are reviewed for various physical systems. As a particular example of a composite system the deuteron is considered, where a theoretical description is discussed in which the electromagnetic interaction and dynamics can be treated in a consistent way. The role of relativity is studied for the various electromagnetic deuteron structure functions. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

Tjon, J.A. [Institute for Theoretical Physics, University of Utrecht, P.O. Box 80.000, 3508 TA Utrecht (Netherlands)

1995-05-10

252

Phase-space quantization of field theory.

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.

Curtright, T.; Zachos, C.

1999-04-20

253

Spinodal decomposition in quantum field theory

We investigate the dynamics of spinodal decomposition in quantum field theory. We consider a lambdaphi/sup 4/ scalar field with tachyonic mass ..mu../sup 2/<0 which is suddenly brought into contact with a heat bath at zero temperature. By using the two-particle irreducible closed-time-path effective action we give a detailed description of how fluctuations in the infrared end of the spectrum grow to give rise to a Bose--Einstein condensate. The later time behavior of the phase decomposition is described by mean field theory. copyright 1989 Academic Press, Inc.

Calzetta, E.

1989-02-15

254

Conformal field theory on affine Lie groups

Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.

Clubok, K.S.

1996-04-01

255

Field strength formulation of gauge theories

In this thesis an alternative to the usual formulation of gauge theories is presented. The usual description in terms of vector field potentials A/sub ..mu../(x) is replaced by a description in terms of field strength tensors F..mu../sub v/(x). This is done in the coordinate gauge, x..mu..A/sub ..mu../(x) = 0, where the vector potentials can be expressed in a simple form in terms of the field strengths. The inversion formula gives a one-to-one correspondence between smooth fields A/sub ..mu../ and F/sub ..mu..v/. Even for singular A/sub ..mu../ configurations, it has been shown that the set of potentials which corresponds to the same F/sub ..mu..v/ (copies) is probably of measure zero in the space of potentials. Furthermore, the field strength tensor in the coordinate gauge has to satisfy the Bianchi identities. As a result the generating functional Z(J) for the quantum field theory may be transformed from an expression in terms of A..mu..(x) to one in terms of fields lambda(sub sigma)x can be introduced to enforce these constraints. The tensor fields F/sub ..mu..v/(x). The Bianchi identities appear as constraints on the allowed class of tensors F/sub ..mu..v(x). A set of Lagrange multiplier fields lambda/sub sigma/(x) can be introduced to enforce these constraints. The tensor fields F/sub ..mu..v/(x) can be integrated out in the functional integral for Z, leaving an expression for Z(J) in terms of the fields lambdasigma(x). This appears to be useful for analyzing the strong coupling limit of the gauge theory. Our results are closely related to, but are much simpler than, Halpern's dual variable formulation of gauge theories in the axial gauge. The Hamiltonian formalism for systems with constraints corresponding to this field strength formulation was also developed for the abelian theory. The results show that the field strength formulation of the gauge theory can be seen as defining a new quantum theory in its own right.

Mendel, E.D.

1982-01-01

256

Knots, topology and quantum field theories

The title of the workshop, Knots, Topology and Quantum Field Theory, accurate reflected the topics discussed. There have been important developments in mathematical and quantum field theory in the past few years, which had a large impact on physicist thinking. It is historically unusual and pleasing that these developments are taking place as a result of an intense interaction between mathematical physicists and mathematician. On the one hand, topological concepts and methods are playing an increasingly important lead to novel mathematical concepts: for instance, the study of quantum groups open a new chapter in the deformation theory of Lie algebras. These developments at present will lead to new insights into the theory of elementary particles and their interactions. In essence, the talks dealt with three, broadly defined areas of theoretical physics. One was topological quantum field theories, the other the problem of quantum groups and the third one certain aspects of more traditional field theories, such as, for instance, quantum gravity. These topics, however, are interrelated and the general theme of the workshop defies rigid classification; this was evident from the cross references to be found in almo all the talks.

Lusanna, L. (Florence Univ. (Italy))

1989-01-01

257

"Quantum Field Theory and QCD"

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.

Jaffe, Arthur M.

2006-02-25

258

Axiomatic quantum field theory. Jet formalism

Jet formalism provides the adequate mathematical formulation of classical field theory, reviewed in hep-th\\/0612182v1. A formulation of QFT compatible with this classical one is discussed. We are based on the fact that an algebra of Euclidean quantum fields is graded commutative, and there are homomorphisms of the graded commutative algebra of classical fields to this algebra. As a result, any

G. Sardanashvily

2007-01-01

259

Modified Hamiltonian formalism for higher-derivative theories

An alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach, it has the following advantages: (i) The Lagrangian, when expressed in terms of new variables, yields proper equations of motion; no additional Lagrange multipliers are necessary. (ii) The Legendre transformation can be performed in a straightforward way, provided the Lagrangian is nonsingular in the Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.

Andrzejewski, K.; Gonera, J.; Machalski, P.; Maslanka, P. [Department of Theoretical Physics II, University of Lodz, Pomorska 149/153, 90-236 Lodz (Poland)

2010-08-15

260

A Lagrangian particle model has been adapted to examine human exposures to particulate matter ? 10 µm (PM10) in agricultural settings. This paper reports the performance of the model in comparison to extensive measurements by elastic LIDAR (light detection and ranging). For the first time, the LIDAR measurements allowed spatially distributed and time dynamic measurements to be used to test

Junming Wang; April L. Hiscox; David R. Miller; Thomas H. Meyer; Ted W. Sammis; Jack Dibb; Robert Griffin; William Brune; Maxwell Shauck; Martin Buhr; Philip Lupo; Elaine Symanski; John Richards; Todd Brozell; Charles Rea; Geoff Boraston; John Hayden; Alberto Escrig; Eliseo Monfort; Irina Celades; Xavier Querol; Fulvio Amato; María Minguillon; Philip Hopke; Naresh Kumar; Veronica Nixon; Kaushik Sinha; Xiaosen Jiang; Sarah Ziegenhorn; Thomas Peters; Xianghui Nie; Guo Huang; Yongping Li; Ravi Bhardwaj; Xihua Chen; Radisav Vidic; Yung-Chen Yao; Jiun-Horng Tsai; Hui-Fen Ye; Hung-Lung Chiang; Ami Zota; Robert Willis; Rebecca Jim; Gary Norris; James Shine; Rachelle Duvall; Laurel Schaider; John Spengler; Hai Zhang; Raymond Hoff; Jill Engel-Cox; David Miller

2009-01-01

261

Noncommutative Geometry in M-Theory and Conformal Field Theory

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.

Morariu, Bogdan

1999-05-01

262

Non Perturbative Aspects of Field Theory

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.

Bashir, A. [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacn 58040 (Mexico)

2009-04-20

263

Staircase models from affine Toda field theory

The authors propose a class of purely elastic scattering theories generalizing the staircase model of Al. B. Zamolodchikov, based on the affine Toda field theories for simply-laced Lie algebras g = A,D,E at suitable complex values of their coupling constants. Considering their Thermodynamic Bethe Ansatz equations, they give analytic arguments in support of a conjectured renormalization group flow visiting the neighborhood of each W[sub g] minimal model in turn.

Dorey, P. (Service de Physique Theorique de Saclay, Gif-sur-Yvette (France)); Ravanini, F. (INFN, Bologna (Italy))

1993-02-20

264

Tachyon condensation in string field theory

It has been conjectured that at a stationary point of the tachyon potential for the D-brane of bosonic string theory, the negative energy density exactly cancels the D-brane tension. We evaluate this tachyon potential by off-shell calculations in open string field theory. Surprisingly, the condensation of the tachyon mode alone into the stationary point of its cubic potential is found

Ashoke Sen; Barton Zwiebach

2000-01-01

265

Quantum field theory of treasury bonds

NASA Astrophysics Data System (ADS)

The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.

Baaquie, Belal E.

2001-07-01

266

Tachyon condensation in superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the D-brane–anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess–Zumino–Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by

Nathan Berkovits; Ashoke Sen; Barton Zwiebach

2000-01-01

267

Auxiliary fields in open gauge theories

NASA Astrophysics Data System (ADS)

We show that for open gauge theories, it is possible to build an off-shell Becchi-Rouet-Stora-Tyutin algebra together with an invariant extension of the classical action. This is based on the introduction of auxiliary fields, after having defined an on-shell invariant quantum action, where the gauge-fixing action is written as in Yang-Mills type theories up to a modified Becchi-Rouet-Stora-Tyutin operator. An application to simple supergravity is performed.

Djeghloul, N.; Meziane, A.; Tahiri, M.

2013-09-01

268

Effective Field Theory and Precision Electroweak Measurements

NASA Astrophysics Data System (ADS)

The first part of these lectures provides a brief introduction to the concepts and techniques of effective field theory. The second part reviews precision electroweak constraints using effective theory methods. Several simple extensions of the Standard Model are considered as illustrations. The appendix contains some new results on the one-loop contributions of electroweak triplet scalars to the T parameter and contains a discussion of decoupling in that case.

Skiba, Witold

2011-03-01

269

Recent progress in irrational conformal field theory

In this talk, I will review the foundations of irrational conformal field theory (ICFT), which includes rational conformal field theory as a small subspace. Highlights of the review include the Virasoro master equation, the Ward identities for the correlators of ICFT and solutions of the Ward identities. In particular, I will discuss the solutions for the correlators of the g/h coset construction and the correlators of the affine-Sugawara nests on g {contains} h{sub 1} {contains} {hor_ellipsis} {contains} h{sub n}. Finally, I will discuss the recent global solution for the correlators of all the ICFT`s in the master equation.

Halpern, M.B.

1993-09-01

270

Tautological relations in Hodge field theory

NASA Astrophysics Data System (ADS)

We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invariants to Gromov Witten invariants. It generalizes the Barannikov Kontsevich construction to the case of higher genera correlators with gravitational descendants. We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological relations. From this perspective the statement that Barannikov Kontsevich construction provides a solution of the WDVV equation looks as the simplest particular case of our theorem. Also it generalizes the particular cases of other low-genera tautological relations proven in our earlier works; we replace the old technical proofs by a novel conceptual proof.

Losev, A.; Shadrin, S.; Shneiberg, I.

2007-12-01

271

A general field-covariant formulation of quantum field theory

NASA Astrophysics Data System (ADS)

In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general field-covariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W=ln Z behave as scalars. We investigate the relation between composite fields and changes of field variables, and we show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as J-dependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variable-changes and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples.

Anselmi, Damiano

2013-03-01

272

What is the simplest quantum field theory?

NASA Astrophysics Data System (ADS)

Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level, the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories and gravity, with gravitational amplitudes exhibiting the best UV behavior at infinite complex momentum. At 1-loop, amplitudes in mathcal{N} = 4 SYM only have scalar box integrals, and it was recently conjectured that the same property holds for mathcal{N} = 8 SUGRA, which plays an important role in the suspicion that this theory may be finite. In this paper we explore and extend the S-matrix paradigm, and suggest that mathcal{N} = 8 SUGRA has the simplest scattering amplitudes in four dimensions. Labeling external states by supercharge eigenstates-Grassmann coherent states-allows the amplitudes to be exposed as completely smooth objects, with the action of SUSY manifest. We show that under the natural supersymmetric extension of the BCFW deformation of momenta, all tree amplitudes in mathcal{N} = 4 SYM and mathcal{N} = 8 SUGRA vanish at infinite complex momentum, and can therefore be determined by recursion relations. An important difference between mathcal{N} = 8 SUGRA and mathcal{N} = 4 SYM is that the massless S-matrix is defined everywhere on moduli space, and is acted on by a non-linearly realized E 7(7) symmetry. We elucidate how non-linearly realized symmetries are reflected in the more familiar setting of pion scattering amplitudes, and go on to identify the action of E 7(7) on amplitudes in mathcal{N} = 8 SUGRA. Moving beyond tree level, we give a simple general discussion of the structure of 1-loop amplitudes in any QFT, in close parallel to recent work of Forde, showing that the coefficients of scalar "triangle" and "bubble" integrals are determined by the "pole at infinite momentum" of products of tree amplitudes appearing in cuts. In mathcal{N} = 4 SYM and mathcal{N} = 8 SUGRA, the on-shell superspace makes it easy to compute the multiplet sums that arise in these cuts by relating them to the best behaved tree amplitudes of highest spin, leading to a straightforward proof of the absence of triangles and bubbles at 1-loop. We also argue that rational terms are absent. This establishes that 1-loop amplitudes in mathcal{N} = 8 SUGRA only have scalar box integrals. We give an explicit expression for 1-loop amplitudes for both mathcal{N} = 4 SYM and mathcal{N} = 8 SUGRA in terms of tree amplitudes that can be determined recursively. These amplitudes satisfy further relations in mathcal{N} = 8 SUGRA that are absent in mathcal{N} = 4 SYM. Since both tree and 1-loop amplitudes for maximally supersymmetric theories can be completely determined by their leading singularities, it is natural to conjecture that this property holds to all orders of perturbation theory. This is the nicest analytic structure amplitudes could possibly have, and if true, would directly imply the perturbative finiteness of mathcal{N} = 8 SUGRA. All these remarkable properties of scattering amplitudes call for an explanation in terms of a "weak-weak" dual formulation of QFT, a holographic dual of flat space.

Arkani-Hamed, Nima; Cachazo, Freddy; Kaplan, Jared

2010-09-01

273

Effective Lagrangians and low energy photon-photon scattering

We use the behavior of the photon-photon scattering for photon energies {omega} less than the electron mass, m{sub e}, to examine the implications of treating the Euler-Heisenberg Lagrangian as an effective field theory. Specifically, we determine the {omega}{sup 2}/m{sub e}{sup 2} behavior of the scattering amplitude predicted by including oneloop corrections to the Euler-Heisenberg effective Lagrangian together with the counterterms required by renormalizability. This behavior is compared with the energy dependence obtained by expanding the exact QED photon-photon scattering amplitude. If the introduction of counterterms in the effective field theory is restricted to those determined by renormalizability, the {omega}{sup 2}/m{sub e}{sup 2} dependences of the two expansions differ. {copyright} {ital 1998} {ital The American Physical Society}

Dicus, D.A. [Center for Particle Physics and Department of Physics, University of Texas, Austin, Texas 78712 (United States); Kao, C. [Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States); Repko, W.W. [Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 (United States)

1998-02-01

274

Extended Hamiltonian systems in multisymplectic field theories

We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the Hamiltonian field equations. In an analogous way to how these systems are defined in the so-called extended (symplectic) formulation of nonautonomous mechanics, we introduce Hamiltonian systems in the extended multimomentum bundle. The geometric properties of these systems are studied, the Hamiltonian equations are analyzed using integrable multivector fields, the corresponding variational principle is also stated, and the relation between the extended and the restricted Hamiltonian systems is established. All these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.

Echeverria-Enriquez, Arturo; Leon, Manuel de; Munoz-Lecanda, Miguel C.; Roman-Roy, Narciso [Departamento de Matematica Aplicada IV, Campus Norte UPC, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona (Spain); Instituto de Matematicas y Fisica Fundamental, CSIC, C/Serrano 123, E-28006 Madrid (Spain); Departamento de Matematica Aplicada IV, Campus Norte UPC, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona (Spain)

2007-11-15

275

Six-dimensional unified field theory

NASA Astrophysics Data System (ADS)

The six-dimensional EM field equations with monopoles formulated by Teli and Palaskar (1984) and Teli (1984) are extended by analogy to encompass the gravitational, Heavisidian, strong, Proca, and weak fields, as well as the weak-field partner field proposed by Singh (1981). Six-dimensional gravito-Heavisidian field equations which are reducible to the standard four-dimensional forms are derived; complex electrogravitational and magneto-Heavisidian fields are formed and their six-dimensional field equations obtained; and a full six-dimensional unified field theory is developed by neglecting the masses of the field-exchange particles and assuming that the strong and weak fields satisfy curl equations as well as the divergence equations given by Singh (1981). The resulting set of equations couples all four basic fields with their partner fields to yield a magneto-Heavisidio-Proca-Singh field arising from a magneto-Heavisidio-Proca-Singh monopole produced by the moving electrogravito-strong-weak charge.

Teli, M. T.

1985-05-01

276

l-REDUCTION and Twisted Conformal Field Theory

NASA Astrophysics Data System (ADS)

Theory of l-reduction of KP hierarchy is investigated from a view point of conformal field theory. Twisted conformal field theory emerges naturally in the discussion. Possible application of this kind of connection between hierarchy and CFT is suggested.

Kato, Hideyuki

277

A new look at electromagnetic field theory

The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field\\u000a as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations\\u000a as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables

Mendel Sachs

1980-01-01

278

Field Strength Formulation of Gauge Theories

In this thesis an alternative to the usual formulation of gauge theories is presented. The usual description in terms of vector field potentials A(,(mu))(x) is replaced by a description in terms of field strength tensors F(,(mu)(nu))(x). This is done in the coordinate gauge, x('(mu))A(,(mu))(x) = 0, where the vector potentials can be expressed in a simple form in terms of

Eduardo David Mendel

1982-01-01

279

Super-Poincaré invariant superstring field theory

Using the topological techniques developed in an earlier paper with Vafa, a field theory action is constructed for any open string with critical N = 2 worldsheet superconformal invariance. Instead of the Chern-Simons-like action found by Witten, this action resembles that of a Wess-Zumino-Witten model. For the N = 2 string which describes (2,2) self-dual Yang-Mills, the string field generalizes

Nathan Berkovits

1996-01-01

280

On marginal deformations in superstring field theory

We use level truncated superstring field theory to obtain the effective potential for the Wilson line marginal deformation parameter which corresponds to the constant vacuum expectation value of the U(1) gauge field on the D-brane in a particular direction. We present results for both the BPS and the non-BPS D-brane. In the case of non-BPS D-brane the effective potential has

Amer Iqbal; Asad Naqvi

2001-01-01

281

Anomalous amplitudes in thermal field theory

NASA Astrophysics Data System (ADS)

In this work, we study some anomalous processes in thermal field theory. When one looks at the small momentum limit of such amplitudes, it appears that this limit is not uniquely defined, but depends on some additional conditions. This property explains the discrepancies found in the litterature for the thermal ?^o? 2? amplitude. We also discuss processes involving the ? field, since they may become important near the chiral phase transition.

Gelis, Francois

1999-10-01

282

Shape Dynamics and Effective Field Theory

NASA Astrophysics Data System (ADS)

Shape dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable from classical general relativity. If taken seriously, it suggests that the space-time geometry picture that underlies general relativity can be replaced by a picture based on spatial conformal geometry. This classically well-understood trading of gauge symmetries opens new conceptual avenues in many approaches to quantum gravity. This paper focusses on the general implications for quantum gravity and effective field theory and considers the application of the shape dynamics picture in the exact renormalization group approaches to gravity, loop- and polymer-quantization approaches to gravity and low energy effective field theories. Also, the interpretation of known results is discussed through the shape dynamics picture, particularly holographic renormalization and the problem of time in canonical quantum gravity.

Koslowski, Tim A.

2013-05-01

283

Braided groups and algebraic quantum field theories

We introduce the notion of a braided group. This is analogous to a supergroup with Bose-Fermi statistics ±1 replaced by braid statistics. We show that every algebraic quantum field theory in two dimensions leads to a braided group of internal symmetries. Every quantum group can be viewed as a braided group.

Shahn Majid

1991-01-01

284

Temperature corrections to conformal field theory

We consider finite temperature dynamical correlation functions in the interacting delta-function Bose gas. In the low-temperature limit the asymptotic behaviour of correlation functions can be determined from conformal field theory. In the present work we determine the deviations from conformal behaviour at low temperatures.

F. H. L. Eßler; V. E. Korepin; F. T. Latrémolière

1998-01-01

285

Temperature corrections to conformal field theory

: We consider finite temperature dynamical correlation functions in the interacting delta-function Bose gas. In the low-temperature\\u000a limit the asymptotic behaviour of correlation functions can be determined from conformal field theory. In the present work\\u000a we determine the deviations from conformal behaviour at low temperatures.

F. H. L. Eßler; Vladimir E. Korepin; F. T. Latrémolière

1998-01-01

286

A Modern Introduction to Quantum Field Theory

This book gives a clear exposition of quantum field theory at the graduate level and the contents could be covered in a two semester course or, with some effort, in a one semester course. The book is well organized, and subtle issues are clearly explained. The margin notes are very useful, and the problems given at the end of each

R Parthasarathy

2005-01-01

287

KAM Theorem and Quantum Field Theory.

National Technical Information Service (NTIS)

We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale by scale. The c...

J. Bricmont K. Gawedzki A. Kupiainen

1998-01-01

288

Force Potentials in Quantum Field Theory

As early as 1935 Yukawa conjectured that the nuclear force, which ties together the component nucleons into a solid nucleus, could be attributed to an intermediate field with an intrinsic mass corresponding to the range of the nuclear force. The general success of the meson theory that followed the discovery of such particles in cosmic rays, has been so great

Y. Nambu

1950-01-01

289

Gravitational renormalization of quantum field theory

We propose to include gravity in quantum field theory non-perturbatively by modifying the propagators so that each virtual particle in a Feynman graph move in the space-time determined by the momenta of the other particles in the same graph. By making additional working assumptions, we are able to put this idea at work and obtain a modified Feynman propagator for

Roberto Casadio

2008-01-01

290

Space-time resolved quantum field theory

We have solved simplified model versions of the time-dependent Dirac and Yukawa equation numerically to study the time evolution of electrons, positrons and photons with full spatial resolution. The goal is to better understand how various particle creation and annihilation processes that require quantum field theory can be visualized. There are many open ended questions that we will address. Are

R. Grobe

2009-01-01

291

Dirac-Kaehler Theory and Massless Fields

Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.

Pletyukhov, V. A. [Kosmonavtov av. 21, Brest, 224016 BELARUS (Belarus); Strazhev, V. I. [Nezavisimosti av. 4, Minsk, 220030 (Belarus)

2010-03-24

292

Soliton Solutions in Quantum Field Theory.

National Technical Information Service (NTIS)

It is a present problem of quantum field theory to interpret the soliton solutions of the classical Euler equations. The traditional way requires the quantization of these solutions. The boson method leads to a different approach to the problem. In the fr...

C. Zenses

1979-01-01

293

Classical Cellular Automata and Quantum Field Theory

NASA Astrophysics Data System (ADS)

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics, and an essential role for the gravitational force in these considerations is suspected.

't Hooft, Gerard

2011-11-01

294

Analogue gravity from field theory normal modes?

We demonstrate that the emergence of a curved spacetime `effective Lorentzian geometry' is a common and generic result of linearizing a classical scalar field theory around some non-trivial background configuration. This investigation is motivated by considering the large number of `analogue models' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is

Carlos Barceló; Stefano Liberati; Matt Visser

2001-01-01

295

Siegel Gauge in Vacuum String Field Theory

We study the star algebra of ghost sector in vacuum string field theory (VSFT). We show that the star product of two states in the Siegel gauge is BRST exact if we take the BRST charge to be the one found in Hata and Kawano, and the BRST exact states are nil factors in the star algebra. By introducing a

Kazumi Okuyama

2002-01-01

296

Conformal Field Theory as a Nuclear Functor

We consider Segal's categorical approach to conformal field theory (CFT). Segal constructed a category whose objects are finite families of circles, and whose morphisms are Riemann surfaces with boundary compatible with the families of circles in the domain and codomain. A CFT is then defined to be a functor to the category of Hilbert spaces, preserving the appropriate structure. In

Richard Blute; Prakash Panangaden; Dorette Pronk

2007-01-01

297

Effective field theory of gravity for extended objects

Using effective field theory (EFT) methods we present a Lagrangian formalism which describes the dynamics of nonrelativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: r{sub s}, the size of the compact objects, r, the orbital radius, and r/v, the wavelength of the physical radiation (where the velocity v is the expansion parameter). In the EFT, radiation is systematically included in the v expansion without the need to separate integrals into near zones and radiation zones. Using the EFT, we show that the renormalization of ultraviolet divergences which arise at v{sup 6} in post-Newtonian (PN) calculations requires the presence of two nonminimal worldline gravitational couplings linear in the Ricci curvature. However, these operators can be removed by a redefinition of the metric tensor, so that the divergences arising at v{sup 6} have no physically observable effect. Because in the EFT finite size features are encoded in the coefficients of nonminimal couplings, this implies a simple proof of the decoupling of internal structure for spinless objects to at least order v{sup 6}. Neglecting absorptive effects, we find that the power counting rules of the EFT indicate that the next set of short distance operators, which are quadratic in the curvature and are associated with tidal deformations, does not play a role until order v{sup 10}. These operators, which encapsulate finite size properties of the sources, have coefficients that can be fixed by a matching calculation. By including the most general set of such operators, the EFT allows one to work within a point-particle theory to arbitrary orders in v.

Goldberger, Walter D. [Department of Physics, Yale University, New Haven, Connecticut 06511 (United States); Rothstein, Ira Z. [Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States)

2006-05-15

298

Lagrangian continuum dynamics in ALEGRA.

Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

Wong, Michael K. W.; Love, Edward

2007-12-01

299

Routhian reduction for quasi-invariant Lagrangians

NASA Astrophysics Data System (ADS)

In this paper, we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e., Lagrangians that are invariant up to a total time derivative. We show how functional Routhian reduction can be seen as a particular instance of reduction in a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasicyclic coordinates. As an application, we consider the dynamics of a charged particle in a magnetic field.

Langerock, B.; Cantrijn, F.; Vankerschaver, J.

2010-02-01

300

Quantum stability of chameleon field theories.

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(?/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

Upadhye, Amol; Hu, Wayne; Khoury, Justin

2012-07-23

301

Incorporation of fermions into double field theory

NASA Astrophysics Data System (ADS)

Based on the stringy differential geometry we proposed earlier, we incorporate fermions such as gravitino and dilatino into double field theory in a manifestly covariant manner with regard to O( D, D) T-duality, diffeomorphism, one-form gauge symmetry for B-field and a pair of local Lorentz symmetries. We note that there are two kinds of fermions in double field theory: O( D, D) singlet and non-singlet which may be identified, respectively as the common and the non-common fermionic sectors in type IIA and IIB suergravities. For each kind, we construct corresponding covariant Dirac operators. Further, we derive a simple criterion for an O( D, D) rotation to flip the chirality of the O( D, D) non-singlet chiral fermions, which implies the exchange of type IIA and IIB supergravities.

Jeon, Imtak; Lee, Kanghoon; Park, Jeong-Hyuck

2011-11-01

302

Transformations among large c conformal field theories

NASA Astrophysics Data System (ADS)

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.

Jankiewicz, Marcin; Kephart, Thomas W.

2006-06-01

303

Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology

In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincar\\\\'e invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on

Aiyalam P. Balachandran; Alberto Ibort; Giuseppe Marmo; Mario Martone

2010-01-01

304

Hydrodynamic flow structures in quantum field theory

The transport of matter is examined in the context of relativistic quantum transport theory for the case of neutral scalar fields. The goal is to formulate a theory valid off mass shell and out of equilibrium. We construct a conserved moment tensor which coincides with the ensemble average of the Noether tensor, or the improved energy-momentum tensor within an additive constant of the improvement term. Conditions for closure of the conservation equation are given for the phi/sup 4/ coupling. 8 references.

Carruthers, P.; Zachariasen, F.

1984-05-01

305

Exclusion Statistics in Conformal Field Theory Spectra

NASA Astrophysics Data System (ADS)

We propose a new method for investigating the exclusion statistics of quasiparticles in conformal field theory (CFT) spectra. The method leads to one-particle distribution functions, which generalize the Fermi-Dirac distribution. For the simplest SU\\(n\\) invariant CFTs we find a generalization of Gentile parafermions, and we obtain new distributions for the simplest ZN-invariant CFTs. In special examples, our approach reproduces distributions based on ``fractional exclusion statistics'' in the sense of Haldane. We comment on applications to fractional quantum Hall effect edge theories.

Schoutens, Kareljan

1997-10-01

306

Remarks on twisted noncommutative quantum field theory

We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.

Zahn, Jochen [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)

2006-05-15

307

Magnetic monopoles in field theory and cosmology

NASA Astrophysics Data System (ADS)

The existence of magnetic monopoles is predicted by many theories of particle physics beyond the Standard Model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems, and discuss how experiments carried out in these systems could help us understand the physics of fundamental monopoles.

Rajantie, A.

2012-12-01

308

Conceptual Developments of 20th Century Field Theories

This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their

Tian Yu Cao

1998-01-01

309

Conceptual Developments of 20th Century Field Theories

This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their

Tian Yu Cao

1997-01-01

310

Lagrangian transport experiments in the MLT region

In order to evaluate material transports in the upper mesosphere and lower thermosphere (MLT) region, Lagrangian transport experiments are performed using wind fields simulated by the Kyushu University middle atmosphere general circulation model (Miyahara and Miyoshi, 1997; Miyahara et al, 1993). The Lagrangian mean meridional circulation is different from the residual mean circulation defined by the Transformed Eulerian Mean equation

S. Watanabe; S. Miyahara; Y. Miyoshi

1999-01-01

311

Spacetime Lagrangian formulation of Barbero Immirzi gravity

NASA Astrophysics Data System (ADS)

We shall discuss a new spacetime gauge-covariant Lagrangian formulation of general relativity by means of the Barbero Immirzi SU(2)-connection on spacetime. To the best of our knowledge, the Lagrangian based on SU(2) spacetime fields seems to appear for the first time here.

Fatibene, L.; Francaviglia, M.; Rovelli, C.

2007-08-01

312

Dirac quantization of parametrized field theory

Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary (and in general, curved) foliations of the flat spacetime instead of only the usual flat foliations, by treating the 'embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schroedinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one. This formal Schroedinger picture-based quantization is unitarily equivalent to the standard Heisenberg picture-based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT, unitarily equivalent to the standard Fock quantization, using techniques from loop quantum gravity (LQG) which are powerful enough to supercede the no-go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding-dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints, and group averaging techniques. The difference between the 1+1-dimensional case and the case of higher spacetime dimensions is that for the latter, only finite gauge transformations are defined in quantum theory, not the infinitesimal ones.

Varadarajan, Madhavan [Raman Research Institute, Bangalore 560 080 (India)

2007-02-15

313

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

Weinstein, Marvin; /SLAC

2005-10-19

314

A master functional for quantum field theory

NASA Astrophysics Data System (ADS)

We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional ? does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=ln Z, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to so-called proper fields, which allows us to work without passing through Z, W or ?. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.

Anselmi, Damiano

2013-04-01

315

Spaces of Conformal Theories and String Field Theory

NASA Astrophysics Data System (ADS)

The problems studied in this thesis were motivated by (a) the program of constructing closed bosonic string field theories (CSFTs), and (b) the issue of background independence in string field theory. Certain minimal area metrics on punctured Riemann surfaces can be used to construct a CSFT, if among other things, these metrics are flat around punctures. The theorem proved in Chapter 2 shows that a minimal area metric is flat around punctures, if there exist neighbourhoods of the punctures that are uniquely foliated by the saturating curves of the metric. Since such foliation was expected the theorem moved one closer to verifying that CSFTs can be constructed. Once CSFTs were in hand, background dependence of the string field action engaged interest. This led to a study of covariant derivatives (interchangeably called connections) on the bundle of states of a space of CFTs, the results of which are presented in Chapter 3. The study clarified the general framework for examining spaces of CFTs and this led (a) to the characterization of covariant derivatives by operator forms omega^epsilon, and (b) to the canonical connection types, Gamma ^{D}, c and | c . One expects to be able to (through use of CFT data) infer, from knowledge of an omega^ epsilon characterizing a connection Gamma, most of the interesting properties and off shoots of Gamma. Things fall short of this expectation, somewhat. The shortfall is analyzed with regard to connection coefficients in an eigenbasis of L_0 and | L_0, BPZ metric compatibility, pull backs of connections to the base and curvature. For a test of the ideas in Chapter 3, toroidally compactified theories are an accessible playground and Chapter 4 recounts a visit to these parts. The highpoints are, that nabla ^{KZ}, a connection that arises naturally in such theory spaces, is a Gamma ^{D} type connection with D the unit disc and that nabla^{KZ } becomes the Zamolodchikov connection when pulled back to the base. Chapter 5 is concerned with the perturbative construction of a CFT in the state space of another. The use of parallel transport yields, as expected, a canonical construction manifestly free of divergences. From this perturbative construction, we extract necessary and sufficient conditions for existence of an extension to a theory space. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).

Kirshnan, Ranganathan

316

Some Lagrangians for systems without a Lagrangian

NASA Astrophysics Data System (ADS)

We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.

Nucci, M. C.; Leach, P. G. L.

2011-03-01

317

Polyacetylene and relativistic field-theory models

Connections between continuum, mean-field, adiabatic Peierls-Froehlich theory in the half-filled band limit and known field theory results are discussed. Particular attention is given to the phi/sup 4/ model and to the solvable N = 2 Gross-Neveu model. The latter is equivalent to the Peierls system at a static, semi-classical level. Based on this equivalence we note the prediction of both kink and polaron solitons in models of trans-(CH)/sub x/. Polarons in cis-(CH)/sub x/ are compared with those in the trans isomer. Optical absorption from polarons is described, and general experimental consequences of polarons in (CH)/sub x/ and other conjugated polymers is discussed.

Bishop, A.R.; Campbell, D.K.; Fesser, K.

1981-01-01

318

Gravity Duals for Nonrelativistic Conformal Field Theories

NASA Astrophysics Data System (ADS)

We attempt to generalize the anti de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.

Balasubramanian, Koushik; McGreevy, John

2008-08-01

319

Magnetic fields and density functional theory

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.

Salsbury Jr., Freddie

1999-02-01

320

Superconformal quantum field theory in curved spacetime

NASA Astrophysics Data System (ADS)

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.

de Medeiros, Paul; Hollands, Stefan

2013-09-01

321

Darwinian evolution: The mutation of a weakly relativistic Lagrangian

NASA Astrophysics Data System (ADS)

The work studies Darwin's order-(v/c) 2 approximation to the relativistic interaction of classical charged particles. The first part presents an introduction to the methods of symplectic reduction in the Newtonian two body problem and then applies these to a two-body Darwin interaction. The momentum-dependent interaction of the Darwin system plays an important role in the ability to reduce to a system of one degree of freedom. Circular orbits are sought, and it is shown that two of the three possible orbits are prohibited by velocity conditions. The second part of the work derives a self-consistent Darwin particle theory from a Lagrangian for electromagnetic fields coupled to particles. The resulting particle Lagrangian agrees with previous results. A similar procedure is followed to obtain a Low-Darwin system, coupling the self-consistent Darwin theory to the Vlasov equation.

Krause, Todd Brandon

322

Advances in mean-field dynamo theories

NASA Astrophysics Data System (ADS)

We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.

Pipin, V. V.

2013-07-01

323

Gravitational Descendants in Symplectic Field Theory

It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory\\u000a leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold\\u000a is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants

Oliver Fabert

2011-01-01

324

Topology, Geometry and Quantum Field Theory

NASA Astrophysics Data System (ADS)

This volume covers the proceedings of an international conference held in Oxford in June 2002. In addition to articles arising from the conference, the book also contains the famous as-yet-unpublished article by Graeme Segal on the Definition of Conformal Field Theories. It is ideal as a view of the current state of the art and will appeal to established researchers as well as to novice graduate students.

Tillmann, Ulrike

2004-06-01

325

Field theory in condensed matter physics

Field theory, born as a description of high energy physics, is also used at much lower energies, in condensed matter physics and statistical mechanics. \\\\Ve make a historical survey oC haw this usage cvolvcd, fram the Dirac equation to the presento RESU~tEN. La teoría de campo, inicialmente utilizada en la física de altas energías, se usa también a mucho más

CARLOS A. A. DE

326

Bifurcations in mean-field-theory annealing

In this paper, we investigate bifurcation processes for the mean-field-theory (MFT) annealing applied to traveling-salesman problems (TSPs). Due to the symmetries of the TSP free energy function, some special bifurcations occur: cyclic symmetry breaking bifurcations and reverse symmetry breaking bifurcations. Saddle-node bifurcations also occur. Which type of bifurcation occurs depends on the symmetry of the eigenvector that corresponds to the

Masa-Aki Sato; Shin Ishii

1996-01-01

327

Effective-field theories for heavy quarkonium

This article reviews recent theoretical developments in heavy-quarkonium physics from the point of view of effective-field theories of QCD. We discuss nonrelativistic QCD and concentrate on potential nonrelativistic QCD. The main goal will be to derive Schroedinger equations based on QCD that govern heavy-quarkonium physics in the weak- and strong-coupling regimes. Finally, the review discusses a selected set of applications, which include spectroscopy, inclusive decays, and electromagnetic threshold production.

Brambilla, Nora; Pineda, Antonio; Soto, Joan; Vairo, Antonio [INFN and Dipartimento di Fisica dell'Universita di Milano via Celoria 16, 20133 Milan (Italy); Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia (Spain); INFN and Dipartimento di Fisica dell'Universita di Milano via Celoria 16, 20133 Milan (Italy)

2005-10-15

328

Review of Open Superstring Field Theory

I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. This action resembles a Wess-Zumino-Witten action and can be constructed in a manifestly D=4 super-Poincar\\\\'e covariant manner. This review is based on lectures given at the ICTP Latin-American String School in Mexico City and the Komaba

Nathan Berkovits

2001-01-01

329

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane–anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1\\/2,1) and (2,6). In the first

I. Ya. Aref'eva; A. S. Koshelev; D. M. Belov; P. B. Medvedev

2002-01-01

330

Quasiparticle properties in effective field theory

The quasiparticle concept is an important tool for the description of many-body systems. We study the quasiparticle properties for dilute Fermi systems with short-ranged, repulsive interactions using effective field theory. We calculate the proper self-energy contributions at order (kF\\/Lambda)3, where \\/Lambda is the short-distance scale that sets the size of the effective range parameters and kF the Fermi momentum. The

L. Platter; H.-W. Hammer; U.-G. Meißner

2003-01-01

331

Quasiparticle properties in effective field theory

The quasiparticle concept is an important tool for the description of many-body systems. We study the quasiparticle properties for dilute Fermi systems with short-ranged, repulsive interactions using effective field theory. We calculate the proper self-energy contributions at order (kF\\/?)3, where ? is the short-distance scale that sets the size of the effective range parameters and kF the Fermi momentum. The

L. Platter; H.-W. Hammer; Ulf-G. Meißner

2003-01-01

332

Nonperturbative Causal Light Cone Field Theory

We discuss the implementation of Light Cone Field Theory (LCFT) in the causal Bogoliubov- Epstein-Glaser finite S-matrix formulation. The benefits re sult from the simple vacuum structure of LCFT which make possible calculations of the S-matrix in a perturbative-like manner even in the presence of a nontrivial, nonperturbative vacuum.The interdependence of particle and vacuum properties leads to an iterative scheme

Pierre Grangé; Ernst Werner

2008-01-01

333

The Global Approach to Quantum Field Theory

Bryce Seligman DeWitt (1923–2004), a friend and mentor to many, was a towering figure in the development of the quantum theories of gravity and gauge fields. To appreciate his uniqueness, one must recall the history through which he lived. From DeWitt's birth date through 1965, general relativity (GR) was considered to have so few empirically testable predictions that its practitioners

S A Fulling

2006-01-01

334

On Multi-Point Liouville Field Theory

NASA Astrophysics Data System (ADS)

In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or atleast require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field.

Zarrinkamar, S.; Hassanabadi, H.; Rajabi, A. A.

2013-11-01

335

The mechanical behavior of porous media is largely governed by the interactions among coexisting components. In a companion paper [Int. J. Eng. Sci. 40 (2002) 1807–1833], a continuum theory of multiphase porous media has been developed that is capable of rigorously characterizing these interactions. In this paper, the results previously obtained are used to develop a macroscale model where the

Changfu Wei; Kanthasamy K. Muraleetharan

2002-01-01

336

Classical Theory of Optical Near Field

NASA Astrophysics Data System (ADS)

The main purpose of this chapter is to present the quasi-static picture of an optical field in the vicinity of small-scale material. The quasi-static picture depends on the fact that the induced boundary charge density dominates the optical near field of a small-scale material via Coulomb's law; therefore, such an optical near field is of a non-radiative or longitudinal nature. This simple physics leads to an intuitive understanding, even in complicated systems with magneto- and electro-optical effects. As prerequisites, the definitions of elementary concepts are given: "retardation effect," "diffraction limit," "near field," and "far field." Furthermore, two numerical methods are presented using the minimum degree of freedom of an electromagnetic field; one is described by the scalar potential adequate for a quasi-static system and the other by a dual vector potential for general optical systems. This chapter is restricted to linear optical effects and is a revised version of the article titled by "Classical Theory on Electromagnetic Near Field" in Progress in Nano-Electro-Optics II (Springer-Verlag Berlin Heidelberg, 2004).

Banno, Itsuki

337

Hormetic Electric Field Theory of Pattern Formation

The hormetic morphogen theory of curvature (Fosslien 2009) proposes that hormetic morphogen concentration gradients modulate the synthesis of adenosine triphosphate (ATP) by cells along the gradients (field cells) and thus regulate their proliferation and induce curvature such as vascular wall curvature; however, it is unclear whether such morphogen gradients can also determine the histological pattern of the walls. Here, I propose that the ATP gradients modulate export of H+ by vacuolar H+-ATPase (V-ATPase) located on the surface of field cells and generate extracellular ion concentration gradients, ion currents and electrical fields along the paths of morphogen gradients. In vitro, electrical fields can induce directional migration and elongation of vascular cells and align the cells with their long axis perpendicular to electrical field vectors (Bai et al. 2004). I suggest that likewise, in vivo vascular transmural electrical fields induced by hormetic morphogen concentration gradients can modulate cell shape i.e. cell elongation and cell curvature, and determine cell orientation. Moreover, I suggest that the electrical fields can modulate bidirectional cell migration and cell sorting via dynamic hormetic galvanotaxis analogous to in vitro isoelectric focusing in proton gradients, thus, hormetic morphogen gradients can determine the curvature of vessel walls and their histological patterns.

Fosslien, Egil

2010-01-01

338

Yangian superalgebras in conformal field theory

NASA Astrophysics Data System (ADS)

Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory.The main examples are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;?) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CPN sigma models, while the former are conjecturally dual to supersphere sigma models.

Creutzig, Thomas

2011-08-01

339

We analyze the particle structure of lattice field theories, in particular of lattice gauge theories with matter fields. We introduce and exploit the idea that particle structure in lattice field theory is intimately related to the statistical mechanics of fluctuating random paths and random tubes which arise in random walk and random surface representations of the lattice theories. Our methods

J. Bricmont; J. Fröhlich

1985-01-01

340

Pauli-Villars regulatization of supergravity and field theory anomalies

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.

Gaillard, M.K.

1995-06-01

341

Inverse Problems in Neural Field Theory

NASA Astrophysics Data System (ADS)

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore-Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Potthast, Roland; Graben, Peter Beim

2009-01-01

342

The Boltzmann equation from quantum field theory

NASA Astrophysics Data System (ADS)

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.

Drewes, Marco; Mendizabal, Sebastián; Weniger, Christoph

2013-01-01

343

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar ({sigma}) and vector ({omega}) fields, and isovector vector ({rho}) fields. The theory exhibits a nonlinear realization of SU(2){sub L} x SU(2){sub R} chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.

Serot, Brian D. [Department of Physics and Nuclear Theory Center, Indiana University, Bloomington, IN 47405 (United States)], E-mail: serot@indiana.edu

2007-12-15

344

Abelian Lagrangian algebraic geometry

NASA Astrophysics Data System (ADS)

This paper begins a detailed exposition of a geometric approach to quantization, which is presented in a series of preprints ([23], [24], ...) and which combines the methods of algebraic and Lagrangian geometry. Given a prequantization U (1)-bundle L on a symplectic manifold M, we introduce an infinite-dimensional Kähler manifold \\mathscr P^{\\mathrm{hw}} of half-weighted Planck cycles. With every Kähler polarization on M we canonically associate a map \\mathscr P^{\\mathrm{hw}}\\overset{\\gamma}{\\to}H^{0}(M,L) to the space of holomorphic sections of the prequantization bundle. We show that this map has a constant Kähler angle and its "twisting" to a holomorphic map is the Borthwick-Paul-Uribe map. The simplest non-trivial illustration of all these constructions is provided by the theory of Legendrian knots in S^3.

Gorodentsev, A. L.; Tyurin, A. N.

2001-06-01

345

Webs of Lagrangian tori in projective symplectic manifolds

NASA Astrophysics Data System (ADS)

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.

Hwang, Jun-Muk; Weiss, Richard M.

2013-04-01

346

New mathematical structures in renormalizable quantum field theories

Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the role they can play in future developments.

Dirk Kreimer

2003-01-01

347

Worldline approach to noncommutative field theory

NASA Astrophysics Data System (ADS)

The study of the heat-trace expansion in non-commutative field theory has shown the existence of Moyal non-local Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive at a master formula for the n-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the non-commutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other non-local operators.

Bonezzi, R.; Corradini, O.; Franchino Viñas, S. A.; Pisani, P. A. G.

2012-10-01

348

The effective field theory of dark energy

NASA Astrophysics Data System (ADS)

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.

Gubitosi, Giulia; Piazza, Federico; Vernizzi, Filippo

2013-02-01

349

The effective field theory treatment of quantum gravity

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.

Donoghue, John F. [Department of Physics, University of Massachusetts, Amherst, MA 01003 (United States)

2012-09-24

350

Quantum field theory in stationary coordinate systems

Quantum field theory is examined in stationary coordinate systems in Minkowski space. Preliminary to quantization of the scalar field, all of the possible stationary coordinate systems in flat spacetime are classified and explicitly constructed. Six distinct classes of such systems are found. Of these six, three have (identical) event horizons associated with them and five have Killing horizons. Two classes have distinct Killing and event horizons, with an intervening region analogous to the ergosphere in rotating black holes. Particular representatives of each class are selected for subsequent use in the quantum field theory. The scalar field is canonically quantized and a vacuum defined in each of the particular coordinate systems chosen. The vacuum states can be regarded as adapted to the six classes of stationary motions. There are only two vacuum states found, the Minkowski vacuum in those coordinate systems without event horizons and the Fulling vacuum in those with event horizons. The responses of monopole detectors traveling along stationary world lines are calculated in both the Minkowski and Fulling vacuums. The responses for each class of motions are distinct from those for every other class. A vacuum defined by the response of a detector must therefore not be equivalent in general to a vacuum defined by canonical quantization. Quantization of the scalar field within a rotating wedge is examined. It has not been possible to construct mode functions satisfying appropriate boundary conditions on the surface of the wedge. The asymptotic form of the renormalized stress tensor near the surfaces had been calculated and is found to include momentum terms which represent a circulation of energy within the wedge.

Pfautsch, J.D.

1981-01-01

351

Conformal field theories, representations and lattice constructions

NASA Astrophysics Data System (ADS)

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, ?( ?) andtilde H(? ) respectively, which may be constructed from a suitable even Euclidean lattice ?. Similarly, one may construct lattices? _C andtilde ? _C by analogous constructions from a doubly-even binary codeC. In the case whenC is self-dual, the corresponding lattices are also. Similarly, ?( ?) andtilde H(? ) are self-dual if and only if ? is. We show thatH(? _C ) has a natural “triality” structure, which induces an isomorphismH(tilde ? _C ) ?tilde H(? _C ) and also a triality structure ontilde H(tilde ? _C ). ForC the Golay code,tilde ? _C is the Leech lattice, and the triality ontilde H(tilde ? _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 ?( ?) andtilde H(? ) 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.

Dolan, L.; Goddard, P.; Montague, P.

1996-07-01

352

Effective Field Theory of Hadrons at Finite Temperature.

NASA Astrophysics Data System (ADS)

Hadronic matter at finite temperature is studied with an effective chiral Lagrangian with pions, vector mesons (rho and omega) and axial vector mesons (A_1). The vector and axial vector mesons are included in the Lagrangian as massive Yang-Mills fields of chiral SU(N _{f})_{L}times SU(N _{f})_{R} symmetry. The dispersion relation and the mean free path of pions in hot hadronic matter are obtained from the effective Lagrangian. The pion mass is calculated at finite temperatures with special attention to the chiral limit. The temperature dependence of the effective masses of vector mesons and axial-vector mesons are also examined. The effective masses at finite temperature are determined from the pole positions of the propagators and from the inverses of the static screening lengths. The results may be viewed as an extrapolation of known hadronic interactions to temperatures up to a deconfinement/chiral symmetry restoring transition or crossover. The emission rates for photons from hadronic matter are calculated for the elementary processes pirho topigamma, pipitorho gamma and rhotopi pigamma at T = 100, 150, 200 MeV. The emission rates are compared with those obtained without the A_1 meson. For pi rhotopigamma and pipitorhogamma reactions the photon emission rates are increased with the inclusion of the A_1 meson in intermediate states. There is a small increase of the emission rate from rho meson decay.

Song, Chungsik

353

Drift estimation from a simple field theory

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.

Mendes, F. M.; Figueiredo, A. [Instituto de Fisica, Universidade de Brasilia, CP: 04455, 70919-970-Brasilia (Brazil)

2008-11-06

354

Entropy and correlators in quantum field theory

It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.

Koksma, Jurjen F., E-mail: J.F.Koksma@uu.n [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); NORDITA, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Prokopec, Tomislav [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); NORDITA, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.d [NORDITA, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Institut fur Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany)

2010-06-15

355

Nonlocal field theory model for nuclear matter

Nuclear matter is investigated in the relativistic Hartree approximation to a nonlocal {sigma}-{omega} model containing short distance vertex form factors to simulate an underlying QCD substructure. At the Hartree level only the nucleon momentum dependence of the distributed vertex enters and the resulting finite nonlocal field theory model is solved in Euclidean metric with simple Gaussian forms for the so-called sideways form factors. To reproduce saturated nuclear matter the nonlocal model selects form-factor ranges at the nucleon mass scale.

Mishra, V.K.; Fai, G.; Tandy, P.C. (Center for Nuclear Research, Department of Physics, Kent State University, Kent, Ohio 44242 (United States)); Frank, M.R. (Department of Physics, Hampton University, Hampton, Virginia 23668 (United States) Continuous Electron Beam Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606 (United States))

1992-09-01

356

Gyrating Schrödinger geometries and nonrelativistic field theories

NASA Astrophysics Data System (ADS)

We propose homogeneous metrics of Petrov type III that describe gyrating Schrödinger geometries as duals to some nonrelativistic field theories, in which the Schrödinger symmetry is broken further so that the phase space has a linear dependence of the momentum in a selected direction. We show that such solutions can arise in four-dimensional Einstein-Weyl supergravity as well as higher-dimensional extended gravities with quadratic curvature terms coupled to a massive vector. In Einstein-Weyl supergravity, the gyrating Schrödinger solutions can be supersymmetric, preserving (1)/(4) of the supersymmetry. We obtain the exact Green function in the phase space associated with a bulk free massive scalar.

Lü, H.; Pope, C. N.

2012-09-01

357

Exact integrability in quantum field theory

The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)

Thacker, H.B.

1980-08-01

358

Thermalization of Strongly Coupled Field Theories

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.

Balasubramanian, V. [David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Bernamonti, A.; Copland, N.; Craps, B.; Staessens, W. [Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay Institutes, B-1050 Brussels (Belgium); Boer, J. de [Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam (Netherlands); Keski-Vakkuri, E. [Helsinki Institute of Physics and Department of Physics, FIN-00014 University of Helsinki (Finland); Mueller, B. [Department of Physics and CTMS, Duke University, Durham, North Carolina 27708 (United States); Schaefer, A. [Institut fuer Theoretische Physik, Universitaet Regensburg, D-93040 Regensburg (Germany); Shigemori, M. [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan)

2011-05-13

359

Interacting Quantum Field Theory in de Sitter Vacua

We discuss interacting quantum field theory in de Sitter space and argue that the Mottola-Allen (MA) vacuum ambiguity is an artifact of free field theory. The nature of the nonthermality of the MA vacua is also clarified. We propose analyticity of correlation functions as a fundamental requirement of quantum field theory in curved spacetimes. In de Sitter space, this principle

Martin B. Einhorn; Finn Larsen

2003-01-01

360

Application of Effective Field Theories to Problems in Nuclear and Hadronic Physics

NASA Astrophysics Data System (ADS)

The Effective Field Theory formalism is applied to the study of problems in hadronic and nuclear physics. We develop a framework to study the exclusive two-body decays of bottomonium into two charmed mesons and apply it to study the decays of the C-even bottomonia. Using a sequence of effective field theories, we take advantage of the separation between the scales contributing to the decay processes, 2mb >> mc >> ?QCD. We prove that, at leading order in the EFT power counting, the decay rate factorizes into the convolution of two perturbative matching coefficients and three non-perturbative matrix elements, one for each hadron. We calculate the relations between the decay rate and non-perturbative bottomonium and D-meson matrix elements at leading order, with next-to-leading log resummation. The phenomenological implications of these relations are discussed. At lower energies, we use Chiral Perturbation Theory and nuclear EFTs to set up a framework for the study of time reversal (T) symmetry in one- and few-nucleon problems. We consider T violation from the QCD theta term and from all the possible dimension 6 operators, expressed in terms of light quarks, gluons and photons, that can be added to the Standard Model Lagrangian. We construct the low energy chiral Lagrangian stemming from different TV sources, and derive the implications for the nucleon Electric Dipole Form Factor and the deuteron T violating electromagnetic Form Factors. Finally, with an eye to applications to nuclei with A ? 2, we construct the T violating nucleon-nucleon potential from different sources of T violation.

Mereghetti, Emanuele

361

Bekenstein bound in asymptotically free field theory

For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E){<=}2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. The validity of the Bekenstein bound in the asymptotically free side of the Euclidean ({lambda}{phi}{sup 4}){sub d} scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature {beta}{sup -1} and defined in a compact spatial region without boundaries. Using the effective potential, we discuss the thermodynamic of the model. For low and high temperatures the system presents a condensate. We present the renormalized mean energy E and entropy S for the system and show in which situations the specific entropy satisfies the quantum bound.

Arias, E.; Svaiter, N. F.; Menezes, G. [Centro Brasileiro de Pesquisas Fisicas-CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180 (Brazil); Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, Sao Paulo, SP, 01140-070 (Brazil)

2010-08-15

362

Renormalized thermal entropy in field theory

Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized entropy which is related with the Newton-Wigner position operator. Accordingly, whenever we trace over a region of space, we trace away degrees of freedom that are localized according to Newton-Wigner localization but not in the usual sense. We consider a free scalar field in d+1 spacetime dimensions prepared in a thermal state and we show that our entropy is free of divergences and has a perfectly sound thermodynamic behavior. In the high temperature/big volume limit our results agree with the standard QFT calculations once the divergent contributions are subtracted from the latter. In the limit of low temperature/small volume the entropy goes to zero but with a different dependence on the temperature.

Cacciatori, Sergio L.; Costa, Fabio; Piazza, Federico [Dipartimento di Scienze Fisiche e Matematiche, Universita dell'Insubria, Via Valleggio 11, I-22100 Como (Italy); Institut fuer Quantenoptik und Quanteninformation (IQOQI), Oesterreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090 Wien (Austria); Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 (Canada)

2009-01-15

363

Renormalized thermal entropy in field theory

NASA Astrophysics Data System (ADS)

Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized entropy which is related with the Newton-Wigner position operator. Accordingly, whenever we trace over a region of space, we trace away degrees of freedom that are localized according to Newton-Wigner localization but not in the usual sense. We consider a free scalar field in d+1 spacetime dimensions prepared in a thermal state and we show that our entropy is free of divergences and has a perfectly sound thermodynamic behavior. In the high temperature/big volume limit our results agree with the standard QFT calculations once the divergent contributions are subtracted from the latter. In the limit of low temperature/small volume the entropy goes to zero but with a different dependence on the temperature.

Cacciatori, Sergio L.; Costa, Fabio; Piazza, Federico

2009-01-01

364

Causality Is Inconsistent With Quantum Field Theory

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.

Wolf, Fred Alan [Global Quantum Physics Educational Company, San Francisco CA (United States)

2011-11-29

365

PT-Symmetric Quantum Field Theory

In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) 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.

Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)

2011-09-22

366

PT-Symmetric Quantum Field Theory

NASA Astrophysics Data System (ADS)

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.

Bender, Carl M.

2011-09-01

367

Causality Is Inconsistent With Quantum Field Theory

NASA Astrophysics Data System (ADS)

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.

Wolf, Fred Alan

2011-11-01

368

Towards a quantum field theory of primitive string fields

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.

Ruehl, W., E-mail: wue_ruehl@t-online.de [Technical University of Kaiserslautern, Department of Physics (Germany)

2012-10-15

369

Continuum regularization of quantum field theory

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.

Bern, Z.

1986-04-01

370

Compressible Lagrangian hydrodynamics without Lagrangian cells

The formulation normally used to calculate compressible Lagrangian hydrodynamics in two dimensions is the following. First define a two-dimensional mesh containing a set of Lagrangian cells. Assign each cell a fixed mass. Compute the acceleration of the mesh points and move the points. The volume of the cell changes with the motion of the points. The changes in cell density, energy, and pressure are computed from the changes in volume. Difficulties occur when there are large distortions in the flow that cause similar large distortions in the Lagrangian cells. The usual solution is to somehow adjust the mesh as the calculation proceeds. This involves either moving individual mesh points or actually reconnecting the mesh. In either case, it becomes necessary to remap the mass from the old cells to the new. This necessarily produces some amount of undesirable numerical diffusion. When and how to adjust the mesh and how to accurately remap the mass and other variables so as to minimize numerical diffusion are the problems. One way to eliminate these problems is to abandon the idea of the Lagrangian cell since it is the distortion of the Lagrangian cell that is the cause of all the other problems. We discuss how the conservation equations can be solved directly without resorting to Lagrangian cells, and we give some examples of calculations using this method. Finally, we give details of the calculational method presently being used.

Clark, R.A.

1985-01-01

371

Some mathematical aspects of quantum field theory

NASA Astrophysics Data System (ADS)

In recent years, physics especially Quantum Field Theory has had an enormous impact in mathematics. This thesis mainly contains two different parts of mathematical developments of problems inspired from physics. Firstly, I study Topological Quantum Field Theory and its related topics. Gromov-Witten theory of resolved conifold corresponds to the Chern-Simons theory of unknot. In a series of papers, Labastida, Marino, Ooguri, Vafa, proposed a conjectural description of Chern-Simons theory of special linear quantum group invariants of links. LMOV conjecture could be viewed as a counterpart of Gopakumar-Vafa conjecture. These are actually parts of the big picture, large N Chern-Simons/Topological string duality. In the first chapter of this part, the orthogonal quantum group version of LMOV conjecture is rigorously formulated in mathematics by using the representation of Brauer centralizer algebra. We also obtain formulae of Lichorish-Millet type which could be viewed as the application in knot theory and topology. By using the cabling technique, we obtain a uniform formula of colored Kauffman polynomial for all torus links with all partitions. Combined these together, we are able to prove many interesting cases of this orthogonal LMOV conjecture. In particular we can apply this uniform formula to verify certain case of the conjecture at roots of unity. In fact, these integer coefficients appeared in the original (orthogonal) LMOV conjecture are called the BPS numbers in string theory. In the second chapter of this part, graphic representations of the universal R-matrices has been used to discover the recursion formulae between various quantum group invariants. We study the recursion relations of R-matrices corresponding to the inclusions Uq( sln) ? Uq(sl n+1), Uq(sl k) x Uq(sln--k ) ? Uq(sln), Uq(sln) ? U q(so2n), Uq(so2k) x Uq(sln--k) ? Uq(so2n). As an application, we find the ODE recursion formulae for HOMFLY and Kauffman polynomials. Secondly, I study the Modular Forms in Topology, Elliptic Genera, Loop Space and String Manifolds. In a series of papers, the following results are discovered. By developing modular invariance on certain characteristic forms, several cancellation formulas emerge naturally as the generalization of the original gravity anomaly cancellation formulas obtained by L. Alvarez-Gaume and E. Witten in their celebrated paper [2] studying the string theory. These cancellation formulae directly imply the divisibility and the congruence phenomena of characteristic numbers by Atiyah-Singer Index theorem, which plays important roles both in topology and differential geometry. We recover the Hirzebruch divisibility of twist signature and obtain the twist higher Rokhlin congruence by applying the modular invariance properties on the elliptic forms and also prove that it is best possible by studying examples constructed from K3-surface and Bott manifold. We also obtain the divisibility results for the index of double twist signature operators. By studying the "modular transgression" on elliptic forms, we obtain some modularly invariant secondary characteristic forms on odd dimensional manifolds. Also, by using this method, we heuristically calculate the Chern-Simons forms for flat bundles over free loop space. This direction is pioneered by Witten [94), who heuristically interpreted the Landweber-Stong elliptic genus as the index of the formal signature operator on free loop space as well as introduced the formal equivariant index of the Dirac operator on loop space, known as Witten operator. We call a manifold to be string if its loop space is spin. It's known that a string manifold is a spin manifold with vanishing half first Pontryagin class. Using the arithmetic properties of Jacobi-Theta functions, we prove the vanishing of the Witten genus of certain nonsingular string complete intersections in products of complex projective spaces, which generalizes a known result of Landweber and Stong [54].

Chen, Qingtao

372

Four-dimensional deformed special relativity from group field theories

We derive a scalar field theory of the deformed special relativity type, living on noncommutative {kappa}-Minkowski space-time and with a {kappa}-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF theory in 4 space-time dimensions. This is done at a nonperturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the noncommutative field theory governs their effective dynamics.

Girelli, Florian [SISSA, Via Beirut 2-4, 34014 Trieste, Italy and INFN, Sezione di Trieste (Italy); School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon (France); Oriti, Daniele [Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, Ontario N2L 2Y5 (Canada); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, Utrecht 3584 TD (Netherlands); Albert Einstein Institute, Am Muehlenberg 4, Golm (Germany)

2010-01-15

373

Continuum and discretum—Unified field theory and elementary constants

NASA Astrophysics Data System (ADS)

Unitary field theories and “SUPER-GUT” theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian (1 3) ) structured vacuum according the quantum theory of unitary fields (Dirac, (4,5) and Heisenberg (6 8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against “all transformations” and which “depend on nothings” (Planck (9 11) ). A satisfactory unitary theory has to involve these constants like the mathematical numbers. Today, Planck's conception of the three elementary constants ?, c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also. According to Popper's theory (12 16) of induction, such unitary theories are “universal explaining theories.” The fundamental constants involve the complementarity between the universal statements in unitary theory and the “basic statements” in the language of classical observables.

Treder, Hans-Jürgen

1992-03-01

374

Hidden gravity in open-string field theory

We clarify the nature of the graviton as a bound state in open-string field theory: The flat metric in the action appears as the vacuum value of an [ital open] string field. The bound state appears as a composite field in the [ital free] field theory.

Siegel, W. (Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794-3840 (United States))

1994-04-15

375

Additive structure of multiplicative subgroups of fields and Galois theory

One of the fundamental questions in current field theory, related to Grothen- dieck's conjecture of birational anabelian geometry, is the investigation of the precise rela- tionship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro-2-Galois groups

Louis Mahe; Jan Min ´; Tara L. Smith

2001-01-01

376

A canopy Lagrangian turbulent scalar transport model for predicting scalar fluxes, sources, and sinks within a forested canopy was tested using CO2 concentration and flux measurements. The model formulation is based on the localized near-field theory (LNF) proposed by Raupach [1989a, b]. Using the measured mean CO2 concentration profile, the vertical velocity variance profile, and the Lagrangian integral timescale profile

Gabriel Katul; Ram Oren; David Ellsworth; Cheng-I. Hsieh; Nathan Phillips; Keith Lewin

1997-01-01

377

Lightcone Quantization of String Theory Duals of Free Field Theories

We quantize in light cone gauge the bosonic sector of string theory on Anti-de Sitter space in the zero curvature radius limit. We find that the worldsheet falls apart into a theory of free partons and map the Hilbert space of the string theory to the Hilbert space of a free scalar in light-front description. We outline how the string

Andreas Karch

2002-01-01

378

The physical renormalization of quantum field theories

NASA Astrophysics Data System (ADS)

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 into the nature of renormalization. I begin 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, ak21,k2 2,k23 , depends on three momentum scales and gives rise to an effective scale Q2effk21 ,k22,k23 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, I discuss some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings.

Binger, Michael William

379

Applying Effective Field Theory to Nuclear Matter.

NASA Astrophysics Data System (ADS)

There has been substantial progress recently in understanding how to apply effective field theory (EFT) methods to nonrelativistic nucleon-nucleon (NN) scattering.(G. P. Lepage, nucl-th/9706029) (U. Van Kolck, hep-ph/9711222) (D. B. Kaplan, M. J. Savage and M. B. Wise, nucl-th/9801034; D. B. Kaplan, nucl-th/9804061) (James V. Steele and R. J. Furnstahl, nucl-th/9802069) Adapting these EFT expansion methods to the nuclear matter problem is a difficult challenge. Here some first steps toward this goal are discussed. The EFT expansion method with cutoff regularization, as proposed by Lepage, is applied to the two-body Bethe-Goldstone equation for the NN interaction in nuclear matter. The nature of short-range correlations in the EFT are discussed and compared to conventional phenomenology.

Tirfessa, Negussie; Furnstahl, R. J.

1998-10-01

380

Mean field theory of charged dendrimer molecules.

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge ? inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations. PMID:22128954

Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat

2011-11-28

381

Winding number in string field theory

NASA Astrophysics Data System (ADS)

Motivated by the similarity between cubic string field theory (CSFT) and the Chern-Simons theory in three dimensions, we study the possibility of interpreting mathcal{N} = left( {{?^2}/3} right)int {{{left( {U{mathcal{Q}_B}{U^{{ - 1}}}} right)}^3}} as a kind of winding number in CSFT taking quantized values. In particular, we focus on the expression of mathcal{N} as the integration of a BRST-exact quantity, mathcal{N} = int {{mathcal{Q}_B}mathcal{A}} which vanishes identically in naive treatments. For realizing non-trivial mathcal{N} , we need a regularization for divergences from the zero eigenvalue of the operator K in the KB c algebra. This regularization must at the same time violate the BRST-exactness of the integrand of mathcal{N} . By adopting the regularization of shifting K by a positive infinitesimal, we obtain the desired value mathcal{N}[{({{text{U}}_{text{tv}}})^{{± {1}}}}] = mp {1} for U tv corresponding to the tachyon vacuum. However, we find that mathcal{N}[{({{text{U}}_{text{tv}}})^{{± {2}}}}] differs from ?2, the value expected from the additive law of mathcal{N} . This result may be understood from the fact that ? = U{mathcal{Q}_B}{U^{{ - 1}}} with U = ( U tv)±2 does not satisfy the CSFT EOM in the strong sense and hence is not truly a pure-gauge in our regularization.

Hata, Hiroyuki; Kojita, Toshiko

2012-01-01

382

Mean field theory of charged dendrimer molecules

NASA Astrophysics Data System (ADS)

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge ? inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.

Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat

2011-11-01

383

Special example of relativistic Hamiltonian field theory

We study fermion-boson bound and scattering states in a (3+1)-dimensional Yukawa theory, using a Tamm-Dancoff truncation of light-front field theory. We retain only two sectors of Fock space, the sector with one fermion and the sector with one fermion and one boson. Such truncations violate Lorentz covariance if one employs the canonical Hamiltonian. In order to restore covariance we modify the Hamiltonian, introducing new terms and allowing all terms to depend on the Fock-space sectors within which or between which they act. In this special example, which is closely related to the Lee model, simple sector-dependent mass and vertex counterterms are sufficient to yield finite observables that are exactly covariant for states whose invariant mass is less than a critical value determined by the cutoffs. Triviality prevents the complete removal of cutoffs from the Hamiltonian that we consider. This calculation illuminates several basic features of the renormalization program required by the nonperturbative light-front Tamm-Dancoff approach.

Glazek, S.D.; Perry, R.J. (Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States))

1992-05-15

384

Dynamical mean-field theory for perovskites

Using the Hubbard Hamiltonian for transition-metal 3{ital d} and oxygen 2{ital p} states with perovskite geometry, we present a dynamical mean-field theory that becomes exact in the limit of large coordination numbers or equivalently large spatial dimensions {ital D}. The theory is based on a description of these systems for large {ital D} using a selective treatment of different hopping processes, which cannot be generated by a unique scaling of the hopping element. The model is solved using a perturbational approach and an extended noncrossing approximation. We discuss the origin of the various 3{ital d} and 2{ital p} bands, the doping dependence of its spectral weight, and the evolution of quasiparticles at the Fermi level upon doping, leading to interesting insight into the dynamical character of the charge carriers near the metal insulator instability of transition-metal oxide systems, three-dimensional perovskites, and other strongly correlated transition-metal oxides. {copyright} {ital 1996 The American Physical Society.}

Lombardo, P. [Laboratoire d`Etudes des Proprietes Electroniques des Solides--CNRS, Boite Postale 166, 38042 Grenoble Cedex 9 (France); Schmalian, J. [Institut fuer Theoretische Physik, Freie Universitaet Berlin, Arnimallee 14, 14195 Berlin (Germany); Avignon, M. [Laboratoire d`Etudes des Proprietes Electroniques des Solides--CNRS, Boite Postale 166, 38042 Grenoble Cedex 9 (France); Bennemann, K. [Institut fuer Theoretische Physik, Freie Universitaet Berlin, Arnimallee 14, 14195 Berlin (Germany)

1996-08-01

385

Hermeneutical Field Theory and the Structural Character of Understanding

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

William Leonard Whitehouse

1991-01-01

386

Quantum equivalence between scalar and antisymmetric tensor field theories

We introduce the concept of a duality transformation for scalar fields. In this way we obtain theories equivalent to scalar theories. Our formalism enables us to study in particular the relation between scalar and antisymmetric tensor field theories on the quantum level.

Mecklenburg, W.; Mizrachi, L.

1984-04-15

387

Hamiltonian constraint in polymer parametrized field theory

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.

Laddha, Alok [Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802-6300 (United States); Chennai Mathematical Institute, SIPCOT IT Park, Padur PO, Siruseri 603103 (India); Raman Research Institute, Bangalore-560 080 (India); Varadarajan, Madhavan [Raman Research Institute, Bangalore-560 080 (India)

2011-01-15

388

The mean field theory for image motion estimation

It is shown how the MFT (mean field theory) can be applied to MRF (Markov random field) model-based motion estimation. Specifically, the motion is characterized by a coupled MRF including a displacement field (motion continuity), a line field (motion discontinuity), and a segmentation field (identifying uncovered areas). These fields are estimated by using the MFT. The efficacy of this approach

J. Zhang; J. Hanauer

1993-01-01

389

Topological field theory of dynamical systems.

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. PMID:23020473

Ovchinnikov, Igor V

2012-09-01

390

Topological and differential geometrical gauge field theory

NASA Astrophysics Data System (ADS)

Recent Quantum Field Theory books have defined the topological charge (Q) in terms of the winding number (N). Contrary to this definition, my proof defines Q in terms of the quantum number (n). Defining Q in terms of n, instead of in terms of N, enables me to determine a precise value for Q. The solutions of all kinds of homotopy classification are referred to as instanton solutions, hence the terms homotopy classification and instanton solution will be used interchangeably. My proof replaces the use of these techniques with the use of the Dirac quantization condition, the covariant Dirac's equation, and the covariant Maxwell's equation. Unlike the earlier approaches, my proof accounts for the concept of the spin quantum number and the concept of time. Using the three methods noted above, my proof yields results not obtained by earlier methods. I have dealt similarly with the Pontryagin Index. I have used the Covariant Electrodynamics, in place of homotopy classification techniques, to create for the Pontryagin Index a proof that is alternative to the one cited in recent literature. The homotopy classification techniques gives an expression that excludes the fact that particles have spin quantum number. Therefore, the homotopy classification techniques does not really describe what the topological charge is in reality. I did derive an expression which does include the spin quantum numbers for particles and this has not been done before. Therefore, this will give a better idea for theoretical physicists about the nature of the topological charge. Contribution to knowledge includes creativity. I created an alternative method to the instanton solution for deriving an expression for the topological charge and this method led to new discoveries as a contribution to knowledge in which I found that topological charge for fermions cannot be quantized (to be quantized means to take discrete values only in integer steps), whereas the instanton solution cannot distinguish between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)

Saaty, Joseph

391

Operator Approach to the Gluing Theorem in String Field Theory.

National Technical Information Service (NTIS)

An algebraic proof of the Gluing Theorem at tree level of perturbation theory in String Field Theory is given. Some applications of the theorem to closed string non-polynomial action are briefly discussed.

A. Abdurrahman J. Bordes C. Lara

1999-01-01

392

An Electrical Spinning Particle In Einstein's Unified Field Theory

Previous work on exact solutions has been shown that sources need to be appended to the field equation of Einstein's unified field theory in order to achieve physically meaningful results,such sources can be included in a variational formulation by Borchsenius and moffat.The resulting field equations and conservation identities related to the theory that can be used to derive the equations

S. N. Pandey; B. K. Sinha; Raj Kumar

2006-01-01

393

Analytic solutions for marginal deformations in open superstring field theory

We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular.

Yuji Okawa; Leonardo Rastelli; Barton Zwiebach

2007-01-01

394

Field-capital theory and its implications for marketing

Purpose – This paper seeks to explore the applicability and implications of Bourdieu's field-capital theory for marketing using original research with a typical European society. Bourdieu's field-capital theory proposes that people acquire economic, social and cultural capital which they deploy in social arenas known as “fields” in order to compete for positions of distinction and status. This exploratory study aims

Alan Tapp; Stella Warren

2010-01-01

395

Field theories in condensed matter physics

NASA Astrophysics Data System (ADS)

In this thesis, field theory is applied to different problems in the context of condensed matter physics. In the first part of this work, a classical problem in which an elastic instability appears is studied. By taking advantage of the symmetries of the system, it is shown that when a soft substrate has a stiff crust and the whole system is forced to reduce its volume, the stiff crust rearranges in a way that will break the initial rotational symmetry, producing a periodic pattern that can be manipulated at our will by suitable changes of the external parameters. It is shown that elastic interactions in this type of systems can be mapped into non-local effective potentials. The possible application of these instabilities is also discussed. In the second part of this work, quantum electrodynamics (QED) is analyzed as an emergent theory that allows us to describe the low energy excitations in two-dimensional nodal systems. In particular, the ballistic electronic transport in graphene-like systems is analyzed. We propose a novel way to control massless Dirac fermions in graphene and systems alike by controlling the group velocity through the sample. We have analyzed this problem by computing transport properties using the transmission matrix formalism and, remarkably, it is found that a behavior conforming with a Snell's-like law emerges in this system: the basic ingredient needed to produce electronic wave guides. Finally, an anisotropic and strongly interacting version of QED 3 is applied to explain the non-universal emergence of antiferromagnetic order in cuprate superconductors. It is pointed out that the dynamics of interacting vortex anti-vortex fluctuations play a crucial role in defining the strength of interactions in this system. As a consequence, we find that different phases (confined and deconfined) are possible as a function of the relative velocity of the photons with respect to the Fermi and gap velocities for low energy excitation in cuprates.

Concha, Andres

396

The gravity duals of {N}=2 superconformal field theories

NASA Astrophysics Data System (ADS)

We study the gauge/gravity duality for theories with four dimensional {N}=2 supersymmetries. We consider the large class of generalized quiver field theories constructed recently by one of us (D.G.). These field theories can also be viewed as the IR limit of M5 branes wrapping a Riemann surface with punctures. We give a prescription for constructing the corresponding geometries and we discuss a few special cases in detail. There is a precise match for various quantities between the field theory and the M-theory description.

Gaiotto, Davide; Maldacena, Juan

2012-10-01

397

On the conformal field theory of the Higgs branch

We study 1+1-dimensional theories of vector and hypermultiplets with (4,4) supersymmetry. Despite strong infrared fluctuations, these theories flow in general to distinct conformal field theories on the Coulomb and Higgs branches. In some cases there may be a quantum Higgs theory even when there is no classical Higgs branch. The Higgs branches of certain such theories provide a framework for

Edward Witten

1997-01-01

398

The Physical Renormalization of Quantum Field Theories

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-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings.

Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC

2007-02-20

399

Mean field theory, topological field theory, and multi-matrix models

We show that the genus zero correlation functions of an arbitrary topological field theory coupled to two-dimensional topological gravity are determined by an appropriate Landau-Ginzburg potential. We determine the potentials that arise for topological sigma models with CP1 or a Calabi-Yau manifold for target space. We present substantial evidence that the multi-matrix models that have been studied recently are equivalent

Robbert Dijkgraaf; Edward Witten

1990-01-01

400

Topological Disorder Operators in Three-Dimensional Conformal Field Theory

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them

Vadim Borokhov; Anton Kapustin; Xinkai Wu

2002-01-01

401

General marginal deformations in open superstring field theory

We construct analytic solutions of open superstring field theory for any exactly marginal deformation in any boundary superconformal field theory when properly renormalized operator products of the marginal operator are given. Our construction is an extension of the general framework for marginal deformations developed in arXiv:0707.4472 for open bosonic string field theory, and the solutions are based on integrated vertex

Michael Kiermaier; Yuji Okawa

2009-01-01

402

MHV, CSW and BCFW: field theory structures in string theory amplitudes

Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three

Rutger Boels; Kasper Jens Larsen; Niels A. Obers; Marcel Vonk

2008-01-01

403

On conformal field theories at fractional levels

For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group M?\\/M. This gives a wealth of conformal data, which we realize as some bosonic theory, in all the ‘regular’ cases. We discuss the generalization to affine theories. As a byproduct, we compute

Ernest Baver; Doron Gepner; Umut Gürsoy

1999-01-01

404

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory.

National Technical Information Service (NTIS)

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it...

M. Weinstein

2005-01-01

405

NASA Astrophysics Data System (ADS)

The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary particle interactions. In this paper, this principle is extended to require additionally the form-invariance of a classical field theory Hamiltonian under variations of the space-time curvature emerging from the gauge fields. This approach is devised on the basis of the extended canonical transformation formalism of classical field theory which allows for transformations of the space-time metric in addition to transformations of the fields. Working out the Hamiltonian that is form-invariant under extended local gauge transformations, we can dismiss the conventional requirement for gauge bosons to be massless in order for them to preserve the local gauge invariance. The emerging equation of motion for the curvature scalar R turns out to be compatible with that from a Proca system in the case of a static gauge field. Communicated by H Stöcker

Struckmeier, J.

2013-01-01

406

Superconformal field theory and Jack superpolynomials

NASA Astrophysics Data System (ADS)

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.

Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre

2012-09-01

407

Gravitational Descendants in Symplectic Field Theory

NASA Astrophysics Data System (ADS)

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 (

Fabert, Oliver

2011-02-01

408

The bases of effective field theories

NASA Astrophysics Data System (ADS)

With reference to the equivalence theorem, we discuss the selection of basis operators for effective field theories in general. The equivalence relation can be used to partition operators into equivalence classes, from which inequivalent basis operators are selected. These classes can also be identified as containing Potential-Tree-Generated (PTG) operators, Loop-Generated (LG) operators, or both, independently of the specific dynamics of the underlying extended models, so long as it is perturbatively decoupling. For an equivalence class containing both, we argue that the basis operator should be chosen from among the PTG operators, because they may have the largest coefficients. We apply this classification scheme to dimension-six operators in an illustrative Yukawa model as well in the Standard Model (SM). We show that the basis chosen by Grzadkowski et al. [5] for the SM satisfies this criterion. In this light, we also revisit and verify our earlier result [6] that the dimension-six corrections to the triple-gauge-boson couplings only arise from LG operators, so the magnitude of the coefficients should only be a few parts per thousand of the SM gauge coupling if BSM dynamics respects decoupling. The same is true of the quartic-gauge-boson couplings.

Einhorn, Martin B.; Wudka, José

2013-11-01

409

Accurate Determination of the Lagrangian Bias for the Dark Matter Halos

NASA Astrophysics Data System (ADS)

We use a new method, the cross-power spectrum between the linear density field and the halo number density field, to measure the Lagrangian bias for dark matter halos. The method has several important advantages over the conventional correlation function analysis. By applying this method to a set of high-resolution simulations of 256^3 particles, we have accurately determined the Lagrangian bias, over 4 mag in halo mass, for four scale-free models with the index n=-0.5, -1.0, -1.5, and -2.0 and three typical cold dark matter models. Our result for massive halos with M>=M_* (M_* is a characteristic nonlinear mass) is in very good agreement with the analytical formula of Mo & White for the Lagrangian bias, but the analytical formula significantly underestimates the Lagrangian clustering for the less massive halos, M

Jing, Y. P.

1999-04-01

410

Lagrangians for plasmas in the drift-fluid approximation

NASA Astrophysics Data System (ADS)

For drift waves and related instabilities, conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in the drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multifluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee that all the conservation laws hold.

Pfirsch, Dieter; Correa-Restrepo, Darío

1997-04-01

411

A new constraint on strongly coupled field theories

We propose a new constraint on the structure of strongly coupled, asymptotically free field theories. The constraint takes the form of an inequality limiting the number of degrees of freedom in the infrared description of a theory relative to the number of underlying, ultraviolet degrees of freedom. We apply the inequality to a variety of theories (both supersymmetric and nonsupersymmetric),

Thomas Appelquist; Andrew G. Cohen; Martin Schmaltz

1999-01-01

412

Phenomenological ideas toward a field theory of matter

A collection of suggestions toward a field theory of matter is presented. Photons which satisfy Maxwell's equations have particle properties when they travel along self trapped orbits. The advantages of the theory are enumerated and include relativistic invariance, pair creation, and wave mechanics. The theory explains why the limiting speed of matter is the velocity of light and high speed

B. Kivel

1979-01-01

413

Self-consistency in relativistic theory of infinite statistics fields

Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. Our previous work has built a relativistic quantum field theory which allows interactions involving infinite statistics particles. In this paper, a more detailed analysis of this theory is available. Topics discussed include cluster decomposition, CPT symmetry and renormalization.

Chao Cao; Yi-Xin Chen; Jian-Long Li

2010-01-01

414

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of new Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed objectively. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics developed here are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2011-12-01

415

NASA Astrophysics Data System (ADS)

The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Rutherford, B.; Montgomery, M. T.

2012-12-01

416

Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program

NASA Astrophysics Data System (ADS)

Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].

Manin, Yuri I.

417

Kinematical Hilbert spaces for fermionic and Higgs quantum field theories

We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also fermions and Higgs fields. This framework is appropriate for coupling matter to quantum gravity. The presence of diffeomorphism invariance forces us to choose a representation which is a

Thomas Thiemann

1998-01-01

418

Unified SemiClassical Field Theory Of Fundamental Interactions

The classical (Electromagnetic) field theory of Maxwell is combined with the Yukawa interaction and with a Collective Shroedinger Equation into a Unified Semi-Classical Field Theory of the four fundamental interactions. The basic ingredient is the following assumption (argument): Range of a finite-range interaction (strong or weak) depends on the total number of baryons involved in the interaction in the same

Krishna Kumar

1996-01-01

419

Interacting field theories in de Sitter space are nonunitary

It is well known that there should be a total cancellation of the IR divergences in unitary interacting field theory, such as QED and gravity. The cancellation should be at all orders between loop and tree-level contributions to cross sections. This is the crucial fact related to the unitarity of the evolution operator (S-matrix) of the underlying interacting field theory.

Emil T. Akhmedov; P. V. Buividovich

2008-01-01

420

A worldsheet description of large N c quantum field theory

The Nc?? limit of a matrix quantum field theory is equivalent to summing only planar Feynman diagrams. The possibility of interpreting this sum as some kind worldsheet theory has been in the air ever since 't Hooft's original paper. We establish here just such a worldsheet description for a scalar quantum field with interaction term gTr?3\\/Nc, and we indicate how

Korkut Bardakci; Charles B. Thorn

2002-01-01

421

Variational description of statistical field theories using Daubechies' wavelets

We investigate the description of statistical field theories using Daubechies' orthonormal compact wavelets on a lattice. A simple variational approach is used to extend mean field theory and make predictions for the fluctuation strengths of wavelet coefficients and thus for the correlation function. The results are compared to Monte Carlo simulations. We find that wavelets provide a reasonable description of

Christoph Best; Andreas Schaefer

1994-01-01

422

Field Theory of Elementary Domains and Particles. I

In S 1 and S 2, a brief historical account was given on the developments in our efforts to construct a unified theory of elementary particles based on the assumption that each particle is a quantum mechanical object extended in space and time. As the most simple model, essential features of field theory are discussed first. Generalization to multilocal field

Yasuhisa Katayama; Hideki Yukawa

1968-01-01

423

On the classical equivalence of superstring field theories

We construct mappings that send solutions of the cubic and non-polynomial open superstring field theories to each other. We prove that the action is invariant under the maps and that gauge orbits are mapped into gauge orbits. It follows that the perturbative spectrum around solutions is the same in both theories. The mappings also preserve the string field reality condition.

Ehud Fuchs; Michael Kroyter

2008-01-01

424

On ramification theory in the imperfect residue field case

This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic p and the cardinality of a p-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse-Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second K-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration.

Zhukov, I B [St. Petersburg State University, St. Petersburg (Russian Federation)

2003-12-31

425

An Algebraic Approach to Quantum Field Theory

It is shown that two quantum theories dealing, respectively, in the Hilbert spaces of state vectors H1 and H2 are physically equivalent whenever we have a faithful representation of the same abstract algebra of observables in both spaces, no matter whether the representations are unitarily equivalent or not. This allows a purely algebraic formulation of the theory. The framework of

Rudolf Haag; Daniel Kastler

1964-01-01

426

Quantum background independence of closed-string field theory

We prove local background independence of the complete quantum closed-string field theory using the recursion relations for string vertices and the existence of connections in CFT theory space. Indeed, with this data we construct an antibracket-preserving map between the state spaces of two nearby conformal theories taking the corresponding string field measured dmu e2S\\/h into each other. A geometrical construction

Ashoke Sen; Barton Zwiebach

1994-01-01

427

Perturbative quantum field theory in the string-inspired formalism

We review the status and present range of applications of the “string-inspired” approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is similar in spirit to string perturbation theory, and bypasses much of the apparatus of standard second-quantized field theory. Its development was initiated by Bern and

Christian Schubert; Chemin de Bellevue

2001-01-01

428

Automatically generating Feynman rules for improved lattice field theories

Deriving the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially when improvement terms are present. This physically important task is, however, suitable for automation. We describe a flexible algorithm for generating Feynman rules for a wide range of lattice field theories including gluons, relativistic fermions and heavy quarks. We also present an efficient implementation of this in a freely available, multi-platform programming language (PYTHON), optimised to deal with a wide class of lattice field theories.

Hart, A. [School of Physics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ (United Kingdom)]. E-mail: a.hart@ed.ac.uk; Hippel, G.M. von [DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom) and Department of Physics, University of Regina, Regina, SK, Canada S4S 0A2 (Canada); Horgan, R.R. [DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Storoni, L.C. [DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2005-10-10

429

On the vacuum state in quantum field theory. II

We want to construct, for every local irreducible quantum field theory which fulfils the spectrum condition, a new theory with the properties:1)It is physically equivalent to the given theory (in the sense ofHaag andKastler).2)The representation space contains a vacuum state.3)The new theory satisfies the spectrum condition.4)For every bounded region\\u000a

H.-J. Borchers

1965-01-01

430

A Possible Way for Constructing Generators of the Poincaré Group in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincaré group only the Hamiltonian and the boost operators carry interactions, we offer an algebraic method to satisfy the Poincaré commutators.We do not need to employ the Lagrangian formalism for local fields with the Nöether representation of the generators. Our approach is based on an opportunity to separate in the primary interaction density a part which is the Lorentz scalar. It makes possible apply the recursive relations obtained in this work to construct the boosts in case of both local field models (for instance with derivative couplings and spins ? 1) and their nonlocal extensions. Such models are typical of the meson theory of nuclear forces, where one has to take into account vector meson exchanges and introduce meson-nucleon vertices with cutoffs in momentum space. Considerable attention is paid to finding analytic expressions for the generators in the clothed-particle representation, in which the so-called bad terms are simultaneously removed from the Hamiltonian and the boosts. Moreover, the mass renormalization terms introduced in the Hamiltonian at the very beginning turn out to be related to certain covariant integrals that are convergent in the field models with appropriate cutoff factors.

Shebeko, A. V.; Frolov, P. A.

2012-02-01

431

Quantum field theory of forward rates with stochastic volatility

NASA Astrophysics Data System (ADS)

In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, first when volatility is taken to be a function of the forward rates, and second when volatility is taken to be an independent quantum field. Since volatility is a positive valued quantum field, the full theory turns out to be an interacting nonlinear quantum field theory in two dimensions. The state space and Hamiltonian for the interacting theory are obtained, and shown to have a nontrivial structure due to the manifold moving with a constant velocity. The no arbitrage condition is reformulated in terms of the Hamiltonian of the system, and then exactly solved for the nonlinear interacting case.

Baaquie, Belal E.

2002-05-01

432

The effective Lagrangian of dark energy from observations

NASA Astrophysics Data System (ADS)

Using observational data on the expansion rate of the universe (H(z)) we constrain the effective Lagrangian of the current accelerated expansion. Our results show that the effective potential is consistent with being flat i.e., a cosmological constant; it is also consistent with the field moving along an almost flat potential like a pseudo-Goldstone boson. We show that the potential of dark energy does not deviate from a constant at more than 6% over the redshift range 0 < z < 1. The data can be described by just a constant term in the Lagrangian and do not require any extra parameters; therefore there is no evidence for augmenting the number of parameters of the LCDM paradigm. We also find that the data justify the effective theory approach to describe accelerated expansion and that the allowed parameters range satisfy the expected hierarchy. Future data, both from cosmic chronometers and baryonic acoustic oscillations, that can measure H(z) at the % level, could greatly improve constraints on the flatness of the potential or shed some light on possible mechanisms driving the accelerated expansion. Besides the above result, it is shown that the effective Lagrangian of accelerated expansion can be constrained from cosmological observations in a model-independent way and that direct measurements of the expansion rate H(z) are most useful to do so.

Jimenez, Raul; Talavera, P.; Verde, Licia; Moresco, Michele; Cimatti, Andrea; Pozzetti, Lucia

2012-03-01

433

Comparisons and connections between mean field dynamo theory and accretion disc theory

NASA Astrophysics Data System (ADS)

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.

Blackman, E. G.

2010-01-01

434

Relativistic, quantum theory of spinor particles in a gravitational field

A relativistic quantum theory of spinor particles in a gravitational field is constructed on the basis of Minkowski space and a gravitational field in the spirit of Faraday and Maxwell. Relativistic equations describing the change in the generalized 4-momentum of a particle and its intrinsic angular momentum in a gravitational field are obtained in the semiclassical approximation. It is shown that that all the well-known gravitational effects can be explained by the constructed theory and that the theoretical results agree with the experimental results. It follows naturally from the theory that the vacuum is unstable and that particles are produced in a gravitational field.

Logunov, A.A.; Loskutov, Yu.M.

1986-10-01

435

Variational and conformal structure of nonlinear metric-connection gravitational Lagrangians

NASA Astrophysics Data System (ADS)

We examine the variational and conformal structures of higher-order theories of gravity that are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first-order formalism when applied to these theories may lead consistently to a new method of reduction of order of the associated field equations. We show that the similarity of the field equations that are derived from appropriate actions via this formalism to those produced by Hilbert varying purely metric Lagrangians is not merely formal but is implied by the diffeomorphism covariant property of the associated Lagrangians. We prove that the conformal equivalence theorem of these theories with general relativity plus a scalar field, holds in the extended framework of Weyl geometry with the same forms of field and self-interacting potential but, in addition, there is a new ``source term'' that plays the role of a stress. We point out how these results may be further exploited and address a number of new issues that arise from this analysis.

Cotsakis, Spiros; Miritzis, John; Querella, Laurent

1999-06-01

436

Modeling Field Theory of Higher Cognitive Functions

The chapter discusses a mathematical theory of higher cognitive functions, including concepts, emotions, instincts, understanding, imagination and intuition. Mechanisms of the knowledge instinct are proposed, driving our understanding of the world. Aesthetic emotions and perception of beauty are related to \\

Leonid Perlovsky

2007-01-01

437

Mean Field Theory of a Neural Network.

National Technical Information Service (NTIS)

A single cell theory for the development of selectivity and ocular dominance in visual cortex has been generalized to incorporate more realistic neural networks that approximate the actual anatomy of small regions of cortex. In particular we have analyzed...

L. N. Cooper C. L. Scofield

1988-01-01

438

Quantum Hall Physics Equals Noncommutative Field Theory

In this note, we study a matrix-regularized version of non-commutative U(1) Chern- Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at

Simeon Hellerman; Mark Van Raamsdonk

439

Mean Field Theory for Sigmoid Belief Networks

We develop a mean eld theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean eld theory provides a tractable approximation to the true probability dis-tribution in these networks; it also yields a lower bound on the likelihood of evidence. We demon-strate the utility of this framework on a benchmark problem in statistical pattern recognition|the classi cation

Lawrence K. Saul; Tommi Jaakkola; Michael I. Jordan

1996-01-01

440

Electroweak Sudakov Corrections using Effective Field Theory

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.

Chiu Juiyu; Golf, Frank; Kelley, Randall; Manohar, Aneesh V. [Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States)

2008-01-18

441

The decoupling theorem in effective scalar field theory

We consider decoupling in the context of an effective quantum field theory of two scalar fields with well separated mass scales and a Z{sub 2} x Z{sub 2} symmetry. We first prove, using Wilson`s exact renormalization group equation, that the theory is renormalizable, in the same way that we showed in a previous paper that theories with a single mass scale renormalizable. We then state and prove a decoupling theorem: at scales below the mass of the heavy particle the full theory may be approximated arbitrarily closely by an effective theory of the light particle alone, with naturalness scale the heavy particle mass. We also compare our formulation of effective field theory with the more conventional local formulation. 11 refs.

Ball, R.D. [CERN, Geneve (Switzerland); Thorne, R.S. [Rutherford Appleton Lab., Oxon (United Kingdom)

1995-08-01

442

An Electrical Spinning Particle In Einstein's Unified Field Theory

Previous work on exact solutions has been shown that sources need to be\\u000aappended to the field equation of Einstein's unified field theory in order to\\u000aachieve physically meaningful results,such sources can be included in a\\u000avariational formulation by Borchsenius and moffat.The resulting field equations\\u000aand conservation identities related to the theory that can be used to derive\\u000athe equations

S. N. Pandey; B. K. Sinha; Raj Kumar

2006-01-01

443

New Dynamical Mean-Field Dynamo Theory and Closure Approach

We develop a new nonlinear mean field dynamo theory that couples field growth\\u000ato the time evolution of the magnetic helicity and the turbulent electromotive\\u000aforce, $\\\\emfb$. We show that the difference between kinetic and current\\u000ahelicities emerges naturally as the growth driver when the time derivative of\\u000a$\\\\emfb$ is coupled into the theory. The solutions predict significant field\\u000agrowth

Eric G. Blackman; George B. Field

2002-01-01

444

Spin-Statistics Transmutation in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Spin-statistics transmutation is the phenomenon occurring when a “dressing” transformation introduced for physical reasons (e.g. gauge invariance) modifies the “bare” spin and statistics of particles or fields. Historically, it first appeared in Quantum Mechanics and in semiclassical approximation to Quantum Field Theory. After a brief historical introduction, we sketch how to describe such phenomenon in Quantum Field Theory beyond the semiclassical approximation, using a path-integral formulation of euclidean correlation functions, exemplifying with anyons, dyons and skyrmions.

Marchetti, P. A.

2010-07-01

445

Limits on tunneling theories of strong-field ionization.

It is shown that tunneling theories of ionization by lasers are subject to upper and lower bounds on the Keldysh parameter gamma. The tunneling limit, gamma-->0, applies to ionization by quasistatic electric fields, but not by laser fields. For lasers, the gamma-->0 limit requires a relativistic treatment. Bounds on the applicability of tunneling theories depend on parameters other than gamma, confirming the rule that strong-field phenomena require more than one dimensionless parameter for scaling. PMID:18764323

Reiss, H R

2008-07-22

446

Results in supersymmetric field theory from 3-brane probe in F-theory

Employing Sen's picture of BPS states on a 3-brane probe world-volume field theory in an F-theory background, we determine some selection rules for the allowed spectrum in massless Nf ? 4 SU(2) Seiberg-Witten theory. The spectrum for any Nf ? 4 is consistent with previous conjectures and analysis.

Ansar Fayyazuddin

1997-01-01

447

Testing symmetries in effective models of higher derivative field theories

Higher derivative field theories with interactions raise serious doubts about their validity due to severe energy instabilities. In many cases the implementation of a direct perturbation treatment to excise the dangerous negative-energies from a higher derivative field theory may lead to violations of Lorentz and other symmetries. In this work we study a perturbative formulation for higher derivative field theories that allows the construction of a low-energy effective field theory being a genuine perturbations over the ordinary-derivative theory and having a positive-defined Hamiltonian. We show that some discrete symmetries are recovered in the low-energy effective theory when the perturbative method to reduce the negative-energy degrees of freedom from the higher derivative theory is applied. In particular, we focus on the higher derivative Maxwell-Chern-Simons model which is a Lorentz invariant and parity-odd theory in 2+1 dimensions. The parity violation arises in the effective action of QED{sub 3} as a quantum correction from the massive fermionic sector. We obtain the effective field theory which remains Lorentz invariant, but parity invariant to the order considered in the perturbative expansion.

Reyes, C. Marat [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, 04510 Mexico D.F. (Mexico)

2009-11-15

448

Bits and Pieces in Logarithmic Conformal Field Theory

NASA Astrophysics Data System (ADS)

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

Flohr, Michael A. I.

449

Anomalous Ward Identities in Spinor Field Theories.

National Technical Information Service (NTIS)

The paper considers the model of a spinor field with arbitrary internal degrees of freedom having arbitrary nonderivative coupling to external scalar, pseudoscalar, vector, and axial-vector fields. By carefully defining the S matrix in the interaction pic...

W. A. Bardeen

1969-01-01

450

THE THEORY OF QUANTIZED FIELDS. II

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

J. Schwinger

1951-01-01

451

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field ? which represents a map S3×R?S2 and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf

Antonio F. Rañada

1989-01-01

452

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field varphi which represents a map S 3× R--> S 2 and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions,

Antonio F. Rañada

1989-01-01

453

Perturbative Aspects of Low-Dimensional Quantum Field Theory

We investigate the low-dimensional applications of Quantum Field Theory (QFT), namely Chern-Simons-Witten Theory (CSWT) and Affine Toda Field Theory (ATFT) in 3- and 2- dimensions. We discuss the perturbative aspects of both theories and compare the results to the exact solutions obtained nonperturbatively. For the three dimensions CSWT case, the perturbative term agree with the nonperturbative polynomial invariants up to third order of the coupling constant 1/k. In the two dimensions ATFT, we investigate the perturbative aspect of S-matrices for A{sub 1}{sup (1)} case in eighth order of the coupling constant {beta}.

Wardaya, Asep Y. [Department of Physics, Diponegoro University, Jl. Prof. Soedarto SH, Semarang (Indonesia); Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia); Zen, Freddy P.; Kosasih, Jusak S.; , Triyanta; Hartanto, Andreas [Indonesia Center for Theoretical and Mathematical Physics (ICTMP) (Indonesia); Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia)

2010-06-22

454

Non-unitarity in quantum affine Toda theory and perturbed conformal field theory

There has been some debate about the validity of quantum affine Toda field theory at imaginary coupling, owing to the non-unitarity of the action, and consequently of its usefulness as a model of perturbed conformal field theory. Drawing on our recent work, we investigate the two simplest affine Toda theories for which this is an issue –a2(1) and a2(2). By

Gábor Takács; Gérard Watts

1999-01-01

455

A New Lorentz Violating Nonlocal Field Theory From String-Theory

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.

Ganor, Ori J.

2007-10-04

456

Heavy Quarks, QCD, and Effective Field Theory

The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E#11;ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e#11;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#12;eld theoretic de#12;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.

Thomas Mehen

2012-10-09

457

A class of six-dimensional conformal field theories

We describe a class of six-dimensional conformal field theories that have\\u000asome properties in common with and possibly are related to a subsector of the\\u000atensionless string theories. The latter theories can for example give rise to\\u000afour-dimensional $N = 4$ superconformal Yang-Mills theories upon\\u000acompactification on a two-torus. Just like the tensionless string theories, our\\u000atheories have an $ADE$-classification,

Mans Henningson

2000-01-01

458

Ordinary versus PT-symmetric ?3 quantum field theory

NASA Astrophysics Data System (ADS)

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric ig?3 quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p2+ix3, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian g?3 quantum field theory with those of the PT-symmetric ig?3 quantum field theory. It is shown that while the conventional g?3 theory in d=6 dimensions is asymptotically free, the ig?3 theory is like a g?4 theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.

Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele

2012-04-01

459

Effective field theory: A modern approach to anomalous couplings

NASA Astrophysics Data System (ADS)

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.

Degrande, Céline; Greiner, Nicolas; Kilian, Wolfgang; Mattelaer, Olivier; Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott; Zhang, Cen

2013-08-01

460

Doubled Field Theory, T-Duality and Courant-Brackets

NASA Astrophysics Data System (ADS)

In these lecture notes we give a simple introduction into double field theory. We show that the presence of momentum and winding excitations in toroidal backgrounds of closed string theory makes it natural to consider double field theories. A tool-kit is developed based on the Courant-bracket and generalized Lie derivatives. We construct a background independent action which represents a T-duality covariantization of the Einstein-Hilbert action for gravity coupled to an antisymmetric tensor field and a dilaton.

Zwiebach, Barton

461

Finite deformations of conformal field theory and spacetime geometry

We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell states of a free closed string moving in a flat background. The dynamic equation corresponding to the condition of conformal invariance includes an infinite number of higher order terms, and we give an explicit procedure for their calculation. The symmetries corresponding to equivalence relations of conformal field theory are described. In this framework we show how to perform a nonperturbative analysis in the low-energy limit and prove that it corresponds to the Brans-Dicke theory of gravity interacting with a skew symmetric tensor field.

Pelts, G. (Department of Physics, The Rockefeller University, 1230 York Avenue, New York, New York 10021-6399 (United States))

1995-01-15

462

Gravity Dual for Reggeon Field Theory and Nonlinear Quantum Finance

NASA Astrophysics Data System (ADS)

We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field