Group field theory with noncommutative metric variables.
Baratin, Aristide; Oriti, Daniele
2010-11-26
We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action. PMID:21231377
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Emergent geometry from field theory: Wilson's renormalization group revisited
NASA Astrophysics Data System (ADS)
Kim, Ki-Seok; Park, Chanyong
2016-06-01
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low-energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdSd +2 /CFTd +1 duality conjecture. We claim that the AdS3 /CFT2 duality may be interpreted as Landau-Ginzburg theory combined with Wilson's renormalization group, which introduces vertex corrections into the Landau-Ginzburg theory in the large-Ns limit, where Ns is the number of fermion flavors.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry. PMID:23909305
Dynamical renormalization group approach to relaxation in quantum field theory
NASA Astrophysics Data System (ADS)
Boyanovsky, D.; de Vega, H. J.
2003-10-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.
Functional renormalization group analysis of tensorial group field theories on Rd
NASA Astrophysics Data System (ADS)
Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele
2016-07-01
Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.
NASA Astrophysics Data System (ADS)
Benedetti, Dario; Lahoche, Vincent
2016-05-01
We develop the functional renormalization group formalism for a tensorial group field theory with closure constraint, in the case of a just renormalizable model over U{(1)}\\otimes 6, with quartic interactions. The method allows us to obtain a closed but non-autonomous system of differential equations which describe the renormalization group flow of the couplings beyond perturbation theory. The explicit dependence of the beta functions on the running scale is due to the existence of an external scale in the model, the radius of {S}1≃ U(1). We study the occurrence of fixed points and their critical properties in two different approximate regimes, corresponding to the deep UV and deep IR. Besides confirming the asymptotic freedom of the model, we find also a non-trivial fixed point, with one relevant direction. Our results are qualitatively similar to those found previously for a rank-3 model without closure constraint, and it is thus tempting to speculate that the presence of a Wilson-Fisher-like fixed point is a general feature of asymptotically free tensorial group field theories.
Gravity as an internal Yang-Mills gauge field theory of the Poincaré group.
NASA Astrophysics Data System (ADS)
Hennig, Jörg; Nitsch, Jürgen
1981-10-01
In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.
Crystal Field Theory and the Angular Overlap Model Applied to Hydrides of Main Group Elements.
ERIC Educational Resources Information Center
Moore, E. A.
1990-01-01
Described is how crystal field theory and the angular overlap model can be applied to very simple molecules which can then be used to introduce such concepts as bonding orbitals, MO diagrams, and Walsh diagrams. The main-group compounds are used as examples and a switch to the transition metal complexes. (KR)
NASA Astrophysics Data System (ADS)
Bi, Zhen; Xu, Cenke
2015-05-01
We construct a series of bbosonic-symmetry-protected topological (BSPT) states beyond group cohomology classification using "decorated defects" approach. This construction is based on topological defects of ordinary Landau order parameters, decorated with the bosonic short-range entangled (BSRE) states in (4 k +3 )d and (4 k +5 )d space-time (with k being nonnegative integers), which do not need any symmetry. This approach not only gives these BSPT states an intuitive physical picture, it also allows us to derive the effective field theory for all these BSPT states beyond group cohomology.
Models in Boundary Quantum Field Theory Associated with Lattices and Loop Group Models
NASA Astrophysics Data System (ADS)
Bischoff, Marcel
2012-11-01
In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net {{A}} on the real line together with an element of a unitary semigroup associated with {{A}}. Namely, we compute elements of this semigroup coming from Hölder continuous symmetric inner functions for a family of (completely rational) conformal nets which can be obtained by starting with nets of real subspaces, passing to its second quantization nets and taking local extensions of the former. This family is precisely the family of conformal nets associated with lattices, which as we show contains as a special case the level 1 loop group nets of simply connected, simply laced groups. Further examples come from the loop group net of {Spin(n)} at level 2 using the orbifold construction.
Group field theory as the second quantization of loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2016-04-01
We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the group field theory (GFT) formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
Renormalization group analysis of a Guersey-model-inspired field theory. II
Luetfueoglu, B. C.; Taskin, F.
2007-11-15
Recently a model, which is equivalent to the scalar form of a Guersey model, is shown to be a nontrivial field theoretical model when it is gauged with a SU(N) field. In this paper we study another model that is equivalent to the vector form of the Guersey model. We get a trivial theory when it is coupled with a scalar field. This result changes drastically when it is coupled with an additional SU(N) field. We find a nontrivial field theoretical model under certain conditions.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Using a stochastic field theory to understand group behavior in microswimmer suspensions
NASA Astrophysics Data System (ADS)
Underhill, Patrick; Qian, Yuzhou; Kramer, Peter
Active suspensions of microswimmers appear both in natural biological systems (e.g. bacteria or algae) and in synthetic systems. Even without external forcing they are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active swimmers cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing in conditions where the mean field theory cannot.
Using a stochastic field theory to understand group behavior in microswimmer suspensions
NASA Astrophysics Data System (ADS)
Underhill, Patrick; Qian, Yuzhou; Kramer, Peter
2015-11-01
Active suspensions of microswimmers appear both in natural biological systems (e.g. bacteria or algae) and in synthetic systems. Even without external forcing they are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active swimmers cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing in conditions where the mean field theory cannot.
Derivative expansions of renormaliztion group effective potentials for {phi}{sup 4} field theories
Shepard, J.R.; McNeil, J.A.
1995-10-01
We approximate an exact Renormalization Group (RG) equation for the flow of the effective action of {phi}{sup 4} field theories by including next-to-leading order (NLO) terms in a derivative expansion. This level of approximation allows us to treat effects of wavefunction renormalization which are beyond the scope of the leading order (LO) formulation. We compare calculations based on a {open_quote}latticized {close_quotes} version of our RG equation in 3 Euclidean dimensions directly with Monte Carlo (MC) results and find excellent overall agreement as well as substantial improvement over LO calculations. We solve the continuum form of our equation to find the Wilson fixed point and determine the critical exponent {eta} (0.046). We also find the critical exponents {nu} (0.666) and {omega} (0.735). These latter two are in much improved agreement with {open_quote}world`s best{close_quotes} values com- pared to those obtained at LO (where no prediction for {eta} is possible). We also find that the {open_quote}universal potential{close_quote} determined via MC methods by Tsypin can be understood quantitatively using our NLO RG equations. Careful analysis shows that ambiguities which plague {open_quote}smooth cutoff{close_quotes} formulations do not arise with our RG equations.
NASA Astrophysics Data System (ADS)
Wang, Fa
2010-07-01
Motivated by the recent numerical evidence [Z. Meng, T. Lang, S. Wessel, F. Assaad, and A. Muramatsu, Nature (London) 464, 847 (2010)10.1038/nature08942] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to Z2 gauge field. We apply the projective symmetry group method to classify possible Z2 spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant Z2 states, differed by the value of gauge flux, zero or π , in the elementary hexagon. The zero-flux state is a promising candidate for the observed spin liquid and continuous phase transition into commensurate Néel order. We also derive the critical field theory for this transition, which is the well-studied O(4) invariant theory [A. V. Chubukov, T. Senthil, and S. Sachdev, Phys. Rev. Lett. 72, 2089 (1994)10.1103/PhysRevLett.72.2089; A. V. Chubukov, S. Sachdev, and T. Senthil, Nucl. Phys. B 426, 601 (1994)10.1016/0550-3213(94)90023-X; S. V. Isakov, T. Senthil, and Y. B. Kim, Phys. Rev. B 72, 174417 (2005)10.1103/PhysRevB.72.174417], and has an irrelevant coupling between Higgs and boson fields with cubic power of spatial derivatives as required by lattice symmetry. This is in sharp contrast to the conventional theory [S. Sachdev and N. Read, Int. J. Mod. Phys. B 5, 219 (1991)10.1142/S0217979291000158], where such transition generically leads to incommensurate magnetic order. In this scenario the Z2 spin liquid could be close to a tricritical point. Soft boson modes will exist at seven different wave vectors. This will show up as low-frequency dynamical spin susceptibility peaks not only at the Γ point (the Néel order wave vector) but also at Brillouin-zone-edge center M points and twelve other points. Some simple properties of the
Conserved quantities and renormalization group flows in two-dimensional field theory
NASA Astrophysics Data System (ADS)
Gerganov, Bogomil Enchev
2000-12-01
Several problems in two-dimensional field theory are investigated. The concepts of classical and quantum integrability in two space-time dimensions are presented in the Introduction and a number of algebraic structures associated with integrable systems are described. Some results of conformal field theory (CFT) and perturbed conformal field theory are reviewed. In Chapter 2, the problem of interaction of two-level atoms in fibrillar geometry with electro-magnetic radiation is studied in perturbation theory. A new formalism is developed, representing the atomic spin operators with elementary fermions, and a resemblance between the structures of this model and quantum electrodynamics is established. Although the system studied is not itself integrable, it can be shown that the integrable quantum sine-Gordon model has some validity as an approximate theory. The following two chapters study the properties of several multi-field generalizations of the sine-Gordon model. The Bukhvostov-Lipatov model is studied in Chapter 3. The classical integrability of the fermionic version of the model is established, both in the bulk and on the half line, by explicitly building a conserved charge of Lorentz spin 3. The quantum integrability of the more general double-cosine model is investigated using perturbed CFT. The analysis showed in particular that the conservation law is spoiled at the quantum level on the Bukhvostov-Lipatov submanifold of the parameter space. In Chapter 4 an N-field model is considered-its interaction term being a product of N cosines. For N >= 2 a conservation law of Lorentz spin 3 is found to first order in perturbed CFT on a manifold where the interaction becomes marginal. The integrability of the model on this manifold is further studied using renormalization techniques and for N = 2, 3, and 4, integrable points are found at which the model is equivalent to the bosonized Gross-Neveu model. Finally, the renormalization properties of a class of integrable
Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-23
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context. PMID:25658993
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-01
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4 +1 )D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.
NASA Astrophysics Data System (ADS)
Carballo-Rubio, Raúl; Barceló, Carlos; Garay, Luis J.
2015-04-01
There exists a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free massless particle with helicity ±2. We have recently shown that this theory can be understood as the result of self-coupling, in complete parallelism to the well-known case of general relativity. This special relativistic field theory of gravity exhibits a decoupling of vacuum zero-point energies of matter and passes all the known experimental tests in gravitation. It is explicitly demonstrated that there is no flow of the effective cosmological constant under the action of the renormalization group at one-loop level, while simple symmetry arguments show that this would continue to be true for higher-loop corrections. The important lesson is that just mild local assumptions concerning the nature of the particle mediating the gravitational interactions are enough to motivate theories which are free of the cosmological constant problem.
Gauge groups and matter fields on some models of F-theory without section
NASA Astrophysics Data System (ADS)
Kimura, Yusuke
2016-03-01
We investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 × K3, with one of the K3's chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 × K3's.
ERIC Educational Resources Information Center
Di Salvo, Vincent S.; And Others
1989-01-01
Generated typology of accounts of specific behaviors that cause problems and prevent successful work group meetings. Administered self-reports to participants (N=569). Found problems stemmed from ineffective interpersonal communication skills even though participants attributed problems to task and structural difficulties in premeeting phase.…
NASA Astrophysics Data System (ADS)
Detournay, Stéphane; Hartman, Thomas; Hofman, Diego M.
2012-12-01
We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the two-dimensional conformal group but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near-horizon geometry of any extremal black hole are identical to those of a two-dimensional field theory with chiral scaling. We consider two examples: black holes in warped AdS3 in topologically massive gravity and in string theory. In both cases, the density of states in the two-dimensional field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.
Infinite symmetric groups and combinatorial constructions of topological field theory type
NASA Astrophysics Data System (ADS)
Neretin, Yu A.
2015-08-01
This paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group G, a subgroup K) categories are constructed whose morphisms are two-dimensional surfaces tiled by polygons and coloured in a certain way. A product of morphisms is a gluing together of combinatorial bordisms, and functors from the category of bordisms to the category of Hilbert spaces and bounded operators correspond to unitary representations of G. The construction has numerous variations: instead of surfaces there can also be one-dimensional objects of Brauer diagram type, multidimensional pseudomanifolds, and bipartite graphs. Bibliography: 66 titles.
NASA Astrophysics Data System (ADS)
Holman, Gordon D.
The primary purpose of the Theory and Modeling Group meeting was to identify scientists engaged or interested in theoretical work pertinent to the Max '91 program, and to encourage theorists to pursue modeling which is directly relevant to data which can be expected to result from the program. A list of participants and their institutions is presented. Two solar flare paradigms were discussed during the meeting -- the importance of magnetic reconnection in flares and the applicability of numerical simulation results to solar flare studies.
NASA Technical Reports Server (NTRS)
Holman, Gordon D.
1989-01-01
The primary purpose of the Theory and Modeling Group meeting was to identify scientists engaged or interested in theoretical work pertinent to the Max '91 program, and to encourage theorists to pursue modeling which is directly relevant to data which can be expected to result from the program. A list of participants and their institutions is presented. Two solar flare paradigms were discussed during the meeting -- the importance of magnetic reconnection in flares and the applicability of numerical simulation results to solar flare studies.
NASA Astrophysics Data System (ADS)
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
Exceptional field theory: SL(5)
NASA Astrophysics Data System (ADS)
Musaev, Edvard T.
2016-02-01
In this work the exceptional field theory formulation of supergravity with SL (5) gauge group is considered. This group appears as a U-duality group of D = 7 maximal supergravity. In the formalism presented the hidden global duality group is promoted into a gauge group of a theory in dimensions 7+number of extended directions. This work is a continuation of the series of works for E 8,7,6 , SO (5 , 5) and SL (3) × SL (2) duality groups.
Group theories: relevance to group safety studies.
Benevento, A L
1998-01-01
Promoting safety in the workplace has been attempted in a variety of ways. Increasingly, industries are using groups such as safety teams and quality circles to promote worker safety. Group influences on individual behavior and attitudes have long been studied in the social psychology literature, but the theories have not been commonly found outside the psychology arena. This paper describes the group theories of group polarization, risky shift, social loafing, groupthink and team think and attempts to apply these theories to existing studies that examine work group influences on safety. Interesting parallels were found but only one study examined group influences as their primary focus of research. Since groups are increasingly used for safety promotion, future research on safety that studies group influences with respect to current group theories is recommended. PMID:24441299
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Diffeomorphism groups and anyon fields
Goldin, G.A.; Sharp, D.H.
1995-09-01
We make use of unitary representations of the group of diffeomorphisms of the plane to construct an explicit field theory of anyons. The resulting anyon fields satisfy q-commutators, where q is the well-known phase shift associated with a single counterclockwise exchange of a pair of anyons. Our method uses a realization of the braid group by means of paths in the plane, that transform naturally under diffeomorphisms of R{sup 2}.
ERIC Educational Resources Information Center
Morpurgo, Simone
2007-01-01
The principles of symmetry and group theory are applied to the zero-order wavefunctions associated with the strong-field t[subscript 2g][superscript 2] configuration and their symmetry-adapted linear combinations (SALC) associated with the generated energy terms are derived. This approach will enable students to better understand the use of…
Introduction to Statistical Field Theory
NASA Astrophysics Data System (ADS)
Brézin, Edouard
2010-07-01
1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the φ4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2011-03-15
Nuclear effective field theory (NEFT) including pions in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, {Lambda}, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space up to including O(p{sup 2}), and find the nontrivial fixed points in the {sup 1}S{sub 0} and {sup 3}S{sub 1}-{sup 3}D{sub 1} channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
Naive Theories of Social Groups
ERIC Educational Resources Information Center
Rhodes, Marjorie
2012-01-01
Four studies examined children's (ages 3-10, Total N = 235) naive theories of social groups, in particular, their expectations about how group memberships constrain social interactions. After introduction to novel groups of people, preschoolers (ages 3-5) reliably expected agents from one group to harm members of the other group (rather than…
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Hohm, Olaf; Penas, Victor A.; Riccioni, Fabio
2016-06-01
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O( D, D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O( D, D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
Polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2008-08-15
Free scalar field theory on 2-dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using loop quantum gravity (LQG) type 'polymer' representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation-annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the 'triangulation'-dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non-Fock nature of the representation ensures that the group of conformal isometries as well as that of the gauge transformations generated by the constraints are represented in an anomaly free manner. Semiclassical states can be analyzed at the gauge invariant level. It is shown that 'physical weaves' necessarily underlie such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.
ERIC Educational Resources Information Center
Huetinck, Linda
1996-01-01
Introduces concepts of modern algebraic group theory in the form of a game. Peg boards and rubber bands represent nonnumerical group elements and are manipulated under the operation of reorienting a regular polygon. Symmetry groups are used to explore set properties, as well as commutative and noncommutative operations. (CMS)
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Vertex operator algebras and conformal field theory
Huang, Y.Z. )
1992-04-20
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics.
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Holographic effective field theories
NASA Astrophysics Data System (ADS)
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
Supersymmetric Quantum Field Theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2005-03-01
We consider some supersymmetric multiplets in a purely quantum framework. A crucial point is to ensure the positivity of the scalar product in the Hilbert space of the quantum system. For the vector multiplet we obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. Then we consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
NASA Astrophysics Data System (ADS)
Choy, Ting-Pong
One of the leading problems in condensed matter physics is what state of matter obtain when there is a strong Coulomb repulsion between the electrons. One of the exotic examples is the high temperature superconductivity which was discovered in copper-oxide ceramics (cuprates) over twenty years ago. Thus far, a satisfactory theory is absent. In particular, the nature of the electron state outside the superconducting phase remains controversial. In analogy with the BCS theory of a conventional superconductor, in which the metal is well known to be a Fermi liquid, a complete understanding of the normal state of cuprate is necessary prior to the study of the superconducting mechanism in the high temperature superconductors. In this thesis, we will provide a theory for these exotic normal state properties by studying the minimal microscopic model which captures the physics of strong electron correlation. Even in such a simple microscopic model, striking properties including charge localization and presence of a Luttinger surface resemble the normal state properties of cuprate. An exact low energy theory of a doped Mott insulator will be constructed by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular, a charge 2e bosonic field which is not made out of elemental excitations emerges at low energies. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green function vanishes. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. We show that many of the normal state properties of the cuprates can result from this new charge
Perturbative double field theory on general backgrounds
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Marques, Diego
2016-01-01
We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as S U (2 )≃S3 with H -flux. In the full string theory this corresponds to a Wess-Zumino-Witten background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler, and Lüst. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.
Singularity theory and N = 2 superconformal field theories
Warner, N.P.
1989-01-01
The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs.
Katanin, A. A.
2015-06-15
We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.
Stadler, K M; Yin, Z P; von Delft, J; Kotliar, G; Weichselbaum, A
2015-09-25
We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales. PMID:26451570
NASA Astrophysics Data System (ADS)
Stadler, K. M.; Yin, Z. P.; von Delft, J.; Kotliar, G.; Weichselbaum, A.
2015-09-01
We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1 /3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
Gauge theory of Virasoro-Kac-Moody group
NASA Astrophysics Data System (ADS)
Cho, Y. M.; Zoh, S. W.
1992-10-01
We present a prototype gauge theory of the Virasoro-Kac-Moody symmetry associated with an arbitrary grand unified group G, which could be interpreted as an effective field theory of a colored string. The theory automatically breaks the symmetry down to H⊗U(1), where H is a subgroup of G and U(1) is the Cartan subgroup of the Virasoro group. After the inevitable spontaneous symmetry breaking the particle spectrum of the theory consists of an infinite tower of massive spin-one fields, the massless gauge fields of the unbroken subgroup, and the light scalar fields which become the pseudo-Goldstone fields of the symmetry breaking
Vector field theories in cosmology
Tartaglia, A.; Radicella, N.
2007-10-15
Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so-called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (cosmic defect theory). We show that the latter fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, while other vector theories use much more. The Newtonian limits are also compared. Finally we show that the cosmic defect theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Resolving Witten's superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2014-04-01
We regulate Witten's open superstring field theory by replacing the picturechanging insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A ∞ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Application of group theory to data reduction
Perey, F.G.
1982-09-01
The analysis within the framework of a theory of what was observed in experiments is essential to the testing of theories and is fundamental to physics. It is shown in this report how group theory can be used to provide a general method of data reduction whereby only the laws of a particular theory are used in the analysis of observations. This application of group theory involves introducing a group of transformations of the physical system upon which the observations were made. This group of transformations leaves invariant the entities of the theory corresponding to the observations made but transforms the entities that were not observed from what they are presumed to be in this theory into what they are not, called possibilities for what they are. This group of transformations is called the possibilities-generating group for the entities for which the observations are being reduced. Since possibilities for entities of theories so obtained are functionals of a known group of transformations, the subsequent use of these possibilities in the theories must be made consistent with the theory of representations of groups. There is a well-known invariant associated with functionals of group elements which is invariant with respect to the parametrization of this group. It is the normalized volume measure in the group manifold of the possibilities-generating group. In this report this invariant measure is called the physical probability of the possibilities since it is a probability measure which has a Borel algebra. The above proposed method of data reduction allows us to deal unambiguously with the uncertainties in entities of physical theories obtained from all of the observations made in experiments and the distinction between systematic and statistical uncertainties disappears. Concrete realizations of possibilities-generating groups are given and explanations in group theoretical terms are offered for several important intuitive notions related to probabilities.
String field theory and tachyon field
NASA Astrophysics Data System (ADS)
Yang, Yi
In this thesis, we study Sen's conjecture on tachyon condensation by using string field theories, i.e. boundary string field theory (BSFT) and cubic string field theory (CSFT). In the BSFT side, the first explicit calculation of effective tachyon action for the bosonic string was given by Witten ten years ago and by many other authors in the last two years. It was extended to the superstring case shortly after. In our work, we give an explicit calculation of Green functions for the fermionic fields and compute the effective tachyon action for the superstring. The results we obtain agree with earlier results. We then generalize the BSFT method to one loop level. The tachyon condensation at one loop level is systematically studied, and many interesting results are obtained which verify Sen's conjecture. We also apply this method to the non-orientable theory at one loop level, where the expected divergence cancellation is reproduced and the similar effective tachyon action is obtained. By using the boundary state formalism, we verify the duality between open and closed strings. In the CSFT side, since there is no known solution to this theory, tachyon condensation can only be studied by numerical methods, i.e. level truncation. However, at the tachyon vacuum, CSFT is simplified to vacuum string field theory (VSFT) which has a solution - sliver state. By adding a tachyon vertex to the boundary of the sliver state, we have calculated the effective action.
Introducing Group Theory through Music
ERIC Educational Resources Information Center
Johnson, Craig M.
2009-01-01
The central ideas of postcalculus mathematics courses offered in college are difficult to introduce in middle and secondary schools, especially through the engineering and sciences examples traditionally used in algebra, geometry, and trigonometry textbooks. However, certain concepts in music theory can be used to expose students to interesting…
Group Development: Extending Tuckman's Theory.
ERIC Educational Resources Information Center
Maples, Mary F.
1988-01-01
Presents a framework for extending the Tuckman model of developmental sequence in small groups. Considers Tuckman's stages of forming, storming, norming, performing, and adjourning lacking in descriptive depth and clear definition. Gathered and organized group dynamics graduate students' assessments of characteristics of stages over five-year…
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Applications of Group Theory to Atoms, Molecules, and Solids
NASA Astrophysics Data System (ADS)
Wolfram, Thomas; Ellialtıǧlu, Şinasi
2014-01-01
Preface; 1. Introductory example: squarene; 2. Molecular vibrations of isotopically substituted AB2 molecules; 3. Spherical symmetry and the full rotation group; 4. Crystal field theory; 5. Electron spin and angular momentum; 6. Molecular electronic structure: the LCAO model; 7. Electronic states of diatomic molecules; 8. Transition metal complexes; 9. Space groups and crystalline solids; 10. Application of space group theory: energy bands for the perovskite structure; 11. Applications of space group theory: lattice vibrations; 12. Time reversal and magnetic groups; 13. Graphene; 14. Carbon nanotubes; Appendixes; Index.
An introduction to conformal field theory
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.
2000-04-01
A comprehensive introduction to two-dimensional conformal field theory is given. The structure of the meromorphic subtheory is described in detail, and a number of examples are presented explicitly. Standard constructions such as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Zhu's algebra in classifying highest weight representations is elucidated. The fusion product of two representations and the corresponding fusion rules are defined, and Verlinde's formula is explained. Finally, higher correlation functions are considered, and the polynomial relations of Moore and Seiberg and the quantum group structure of chiral conformal field theory are discussed. The treatment is relatively general and also allows for a description of less well known classes of theories such as logarithmic conformal field theories.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups
NASA Astrophysics Data System (ADS)
Lord, Eric A.
1986-12-01
The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.
The arithmetic theory of algebraic groups
NASA Astrophysics Data System (ADS)
Platonov, V. P.
1982-06-01
CONTENTS Introduction § 1. Arithmetic groups § 2. Adèle groups § 3. Tamagawa numbers § 4. Approximations in algebraic groups § 5. Class numbers and class groups of algebraic groups § 6. The genus problem in arithmetic groups § 7. Classification of maximal arithmetic subgroups § 8. The congruence problem § 9. Groups of rational points over global fields § 10. Galois cohomology and the Hasse principle § 11. Cohomology of arithmetic groups References
Renormalizability of supersymmetric group field cosmology
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2014-03-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
Field-theory methods in coagulation theory
Lushnikov, A. A.
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Field-theory methods in coagulation theory
NASA Astrophysics Data System (ADS)
Lushnikov, A. A.
2011-08-01
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W( Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = { n 1, n 2, ..., n g , ...}, where n g is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional Ψ for the probability W( Q, t). The time evolution of Ψ is described by an equation that is similar to the Schrödinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Transpersonal Group Psychotherapy: Theory, Method, and Community.
ERIC Educational Resources Information Center
Clark, Carlton F. "Perk"
1998-01-01
Transpersonal group psychotherapy is a carpet of theory, technique, and experiences woven from threads of contemporary psychology, mysticism, and a perennial philosophy many centuries old. Introduces the basic concepts of transpersonal group psychotherapy, proposes a model of transpersonal group psychotherapy, discusses the training of…
Theory Loves Practice: A Teacher Researcher Group
ERIC Educational Resources Information Center
Hochtritt, Lisa; Thulson, Anne; Delaney, Rachael; Dornbush, Talya; Shay, Sarah
2014-01-01
Once a month, art educators from the Denver metro area have been gathering together in the spirit of inquiry to explore issues of the perceived theory and daily practice divide. The Theory Loves Practice (TLP) group was started in 2010 by Professors Rachael Delaney and Anne Thulson from Metropolitan State University of Denver (MSU) and now has 40…
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Fundamentals of nonassociative classical field theory
Kurdgelaidze, D.F.
1987-05-01
A nonassociative classical field theory is constructed. Octonion algebra is studied. The octonion is represented as the sum of a quaternion and an associator. The octonion algebra is expanded and Lorentz group generators are specified in terms of octonion bases in one of the subalgebras. Lorentz vectors and spinors are constructed in the nonassociative algebra. The representation of the Lorentz group in terms of spin and the associator is obtained.
Field theory for string fluids
NASA Astrophysics Data System (ADS)
Schubring, Daniel; Vanchurin, Vitaly
2015-08-01
We develop a field theory description of nondissipative string fluids and construct an explicit mapping between field theory degrees of freedom and hydrodynamic variables. The theory generalizes both a perfect particle fluid and pressureless string fluid to what we call a perfect string fluid. Ideal magnetohydrodynamics is shown to be an example of the perfect string fluid whose equations of motion can be obtained from a particular choice of the Lagrangian. The Lagrangian framework suggests a straightforward extension of the perfect string fluid to more general anisotropic fluids describing higher dimensional branes such as domain walls. Other modifications of the Lagrangian are discussed which may be useful in describing relativistic superfluids and fluids containing additional currents.
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
A Review of Group Systems Theory
ERIC Educational Resources Information Center
Connors, Joanie V.; Caple, Richard B.
2005-01-01
The ability to see interpersonal and group processes beyond the individual level is an essential skill for group therapists (Crouch, Bloch & Wanlass, 1994; Dies, 1994; Fuhriman & Burlingame, 1994). In addition to interpersonal therapy models (e.g., Sullivan and Yalom), there are a number of systems theory models that offer a broad array of…
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
Group Chaos Theory: A Metaphor and Model for Group Work
ERIC Educational Resources Information Center
Rivera, Edil Torres; Wilbur, Michael; Frank-Saraceni, James; Roberts-Wilbur, Janice; Phan, Loan T.; Garrett, Michael T.
2005-01-01
Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable…
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
A Field Theory Problem Relating to Questions in Hyperfield Theory
NASA Astrophysics Data System (ADS)
Massouros, Ch. G.
2011-09-01
M. Krasner introduced the notions of the hypefield and the hyperring in 1956. Much later, he constructed the quotient hyperfield/hyperrring, using a field/ring and a subgroup of its multiplicative group/semigroup. The existence of non-quotient hyperfields and hyperrings was an essential question for the self-sufficiency of the theory of hyperfields and hyperrings vis-à-vis that of fields and rings. The momogene hyperfield, which was introduced by the author, is a hyperfield H having the property x - x = H for all x≠0. The existence of non-quotient monogene hyperfields is a hitherto open question. The answer to this question is directly connected with the answer to the question which fields can be expressed as a difference of a subgroup of their multiplicative group from itself and which these subgroups are. These issues, as well as some relevant theorems are presented in this paper.
Rearranging Pionless Effective Field Theory
Martin Savage; Silas Beane
2001-11-19
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
Teaching Group Theory Using Rubik's Cubes
ERIC Educational Resources Information Center
Cornock, Claire
2015-01-01
Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure…
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Effective Field Theory for Jet Processes
NASA Astrophysics Data System (ADS)
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-01
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.
Effective Field Theory for Jet Processes.
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-13
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms. PMID:27232017
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Differential geometry of groups in string theory
Schmidke, W.B. Jr.
1990-09-01
Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1{vert bar}1). The quantum group GL{sub q}(1{vert bar}1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL{sub q}(1{vert bar}1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S{sup 1})/S{sup 1}. We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs.
Effective field theory in nuclear physics
Martin J. Savage
2000-12-12
I review recent developments in the application of effective field theory to nuclear physics. Emphasis is placed on precision two-body calculations and efforts to formulate the nuclear shell model in terms of an effective field theory.
Effective field theory, past and future
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2016-02-01
I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Transformations among large c conformal field theories
NASA Astrophysics Data System (ADS)
Jankiewicz, Marcin; Kephart, Thomas W.
2006-06-01
We show that there is a set of transformations that relates all of the 24 dimensional even self-dual (Niemeier) lattices, and also leads to non-lattice objects some of which can perhaps be interpreted as a basis for the construction of holomorphic conformal field theory. In the second part of this paper, we extend our observations to higher-dimensional conformal field theories build on extremal partition functions, where we generate c=24k theories. We argue that there exists generalizations of the c=24 models based on Niemeier lattices and of the non-Niemeier spin-1 theories. The extremal cases have spectra decomposable into the irreducible representations of the Fischer-Griess Monster. This additional symmetry leads us to conjecture that these extremal theories, as well as the higher-dimensional analogs of the group lattice bases Niemeiers, will eventually yield to a full construction of their associated CFTs. We observe interesting periodicities in the coefficients of extremal partition functions and characters of the extremal vertex operator algebras.
On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants
Naot, Gad
2005-12-15
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semisimple one by taking its semidirect product with its Lie algebra. We find that the standard knot observable (i.e., trace of the holonomy along the knot) essentially vanishes, and yet, the non-semi-simplicity of the gauge group allows us to consider a class of unorthodox observables which breaks gauge invariance at one point and leads to a nontrivial theory on long knots in R{sup 3}. We have two main morals. (1) In the non-semi-simple case there is more to observe in Chern-Simons theory. There might be other interesting non-semi-simple gauge groups to study in this context beyond our example. (2) In the case of an inhomogeneous gauge group, we find that Chern-Simons theory with the unorthodox observable is actually the same as three-dimensional BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. We prove that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
of the underlying chiral algebra and the modular data pertaining to the characters of the representations. Each of the archetypal logarithmic conformal field theories is studied here by first determining its irreducible spectrum, which turns out to be continuous, as well as a selection of natural reducible, but indecomposable, modules. This is followed by a detailed description of how to obtain character formulae for each irreducible, a derivation of the action of the modular group on the characters, and an application of the Verlinde formula to compute the Grothendieck fusion rules. In each case, the (genuine) fusion rules are known, so comparisons can be made and favourable conclusions drawn. In addition, each example admits an infinite set of simple currents, hence extended symmetry algebras may be constructed and a series of bulk modular invariants computed. The spectrum of such an extended theory is typically discrete and this is how the triplet model \\mathfrak {W} (1,2) arises, for example. Moreover, simple current technology admits a derivation of the extended algebra fusion rules from those of its continuous parent theory. Finally, each example is concluded by a brief description of the computation of some bulk correlators, a discussion of the structure of the bulk state space, and remarks concerning more advanced developments and generalizations. The final part gives a very short account of the theory of staggered modules, the (simplest class of) representations that are responsible for the logarithmic singularities that distinguish logarithmic theories from their rational cousins. These modules are discussed in a generality suitable to encompass all the examples met in this review and some of the very basic structure theory is proven. Then, the important quantities known as logarithmic couplings are reviewed for Virasoro staggered modules and their role as fundamentally important parameters, akin to the three-point constants of rational conformal field
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Non-Perturbative Field Theories.
NASA Astrophysics Data System (ADS)
Stephenson, David
Available from UMI in association with The British Library. Requires signed TDF. Some non-perturbative aspects of field theories are studied by applying lattice gauge theory techniques. The low-lying hadronic mass spectrum is calculated numerically using quenched lattice quantum chromodynamics. The results of large numerical simulations performed on a distributed array processor are presented and analysed. Particular emphasis is stressed upon the understanding of systematic and statistical errors in the calculation. In addition, the pion decay constant and the chiral condensate are evaluated. An attempt is made to relate the numerical findings to the experimentally measured quantities. A pioneering attempt to understand Yukawa couplings is discussed. A toy Fermion-Higgs system is studied numerically on a transputer array. Dynamical fermions are included in the investigation of the behavior of the system over a wide range of Yukawa couplings. A phase diagram is found for the model which shows evidence of spontaneous chiral symmetry breaking transitions. Extensions of the model are discussed together some speculations concerning the behaviour of Yukawa couplings in general. The possibility of using the lattice as a model for space-time is investigated by studying the propagation of particles on a fractal lattice. In addition, the use of truncated fractals as novel regulators is studied numerically in the hope that the problem of fermion doubling will be alleviated.
Groups, information theory, and Einstein's likelihood principle
NASA Astrophysics Data System (ADS)
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.
Groups, information theory, and Einstein's likelihood principle.
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts. PMID:27176234
Group theoretical methods and wavelet theory: coorbit theory and applications
NASA Astrophysics Data System (ADS)
Feichtinger, Hans G.
2013-05-01
Before the invention of orthogonal wavelet systems by Yves Meyer1 in 1986 Gabor expansions (viewed as discretized inversion of the Short-Time Fourier Transform2 using the overlap and add OLA) and (what is now perceived as) wavelet expansions have been treated more or less at an equal footing. The famous paper on painless expansions by Daubechies, Grossman and Meyer3 is a good example for this situation. The description of atomic decompositions for functions in modulation spaces4 (including the classical Sobolev spaces) given by the author5 was directly modeled according to the corresponding atomic characterizations by Frazier and Jawerth,6, 7 more or less with the idea of replacing the dyadic partitions of unity of the Fourier transform side by uniform partitions of unity (so-called BUPU's, first named as such in the early work on Wiener-type spaces by the author in 19808). Watching the literature in the subsequent two decades one can observe that the interest in wavelets "took over", because it became possible to construct orthonormal wavelet systems with compact support and of any given degree of smoothness,9 while in contrast the Balian-Low theorem is prohibiting the existence of corresponding Gabor orthonormal bases, even in the multi-dimensional case and for general symplectic lattices.10 It is an interesting historical fact that* his construction of band-limited orthonormal wavelets (the Meyer wavelet, see11) grew out of an attempt to prove the impossibility of the existence of such systems, and the final insight was that it was not impossible to have such systems, and in fact quite a variety of orthonormal wavelet system can be constructed as we know by now. Meanwhile it is established wisdom that wavelet theory and time-frequency analysis are two different ways of decomposing signals in orthogonal resp. non-orthogonal ways. The unifying theory, covering both cases, distilling from these two situations the common group theoretical background lead to the
On the global symmetries of 6D superconformal field theories
NASA Astrophysics Data System (ADS)
Bertolini, Marco; Merkx, Peter R.; Morrison, David R.
2016-07-01
We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.
Gauge field theory of covariant strings
NASA Astrophysics Data System (ADS)
Kaku, Michio
1986-03-01
We present a gauge covariant second-quantized field theory of strings which is explicitly invariant under the gauge transformations generated by the Virasoro algebra. Unlike the old field theory strings [1] this new formulation is Lorentz covariant as well as gauge covariant under the continuous group Diff( S1) and its central extension. We derive the free action: L=Φ(X) †P[i∂ τ-(L 0-1)]PΦ(X) , in the same way that Feynman derived the Schrödinger equation from the path integral formalism. The action is manifestly invariant under the gauge transformation δΦ(X)= limit∑n=1∞ɛ -nL -nΦ(X) , where P is a projection operator which annihilates spurious states. We give three distinct formulations of this operator P to all orders, the first based on extracting the operator from the functional formulation of the Nambu-Goto action, and the second and third based on inverting the Shapovalov matrix on a Verma module. This gauge covariant formulation can be easily extended to the Green-Schwarz superstring [2,3]. One element application of these methods is to re-express the old Neveu-Schwarz-Ramond model as a field theory which is manifestly invariant under space-time supersymmetric transformations.
Group theory aspects of chaotic strings
NASA Astrophysics Data System (ADS)
Groote, S.; Saar, R.
2014-09-01
Chaotic strings are a special type of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. Chaotic strings are generated by the Chebyshev maps T2(phi) and T3(phi). In this paper we connect the Chebyshev maps via the Galois theory to the cyclic groups Z2 and Z3 and give some ideas how this fundamental connection might lead to the emergence of the familiar Lie group structure of particle physics and, finally, even to the emergence of space-time. The Z3-graded cubic and ternary algebras presented here have been introduced by R. Kerner in 1991 and then developed and elaborated in collaboration with many researches. We present here the most important results associated with these papers.
Teaching group theory using Rubik's cubes
NASA Astrophysics Data System (ADS)
Cornock, Claire
2015-10-01
Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure elective based on physical examples. Abstract concepts, such as subgroups, homomorphisms and equivalence relations are explored with the cubes first. In addition to this, conclusions about the cubes can be made through the consideration of algebraic approaches through a process of discovery. The teaching, learning and assessment methods are explored in this paper, along with the challenges and limitations of the methods. The physical use of Rubik's cubes within the classroom and examination will be presented, along with the use of peer support groups in this process. The students generally respond positively to the teaching methods and the use of the cubes.
Palmer, R.B.; Baggett, N.; Claus, J.; Fernow, R.; Stumer, I.; Figueroa, H.; Kroll, N.; Funk, W.; Lee-Whiting, G.; Pickup, M.
1985-04-01
Substantial progress since the Los Alamos Workshop two years ago is reported. A radio-frequency model of a grating accelerator has been tested at Cornell, and extensive calculations compared with observations. Alternative structures consisting of either hemispherical bumps on a plane, or conducting spheres in space, have also been rf modeled. The use of liquid droplets to form such structures has been proposed and a conceptual design studied. Calculations and experiments have examined the effects of surface plasmas, and shown that in this case the reflectivity is low. However, calculations and observations suggest that gradients in excess of 1 GeV/meter should be obtainable without forming such plasma. An examination of wake fields shows that, with Landau damping, these are independent of wavelength. The use of near field structures to act as high gradient focusing elements has been studied and shows promise, independent of the acceleration mechanism. A proposal has been made to establish a facility that would enable ''proof of principle experiments'' to be performed on these and other laser driven accelerator mechanisms. 11 refs., 10 figs.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Canonical quantization of Galilean covariant field theories
NASA Astrophysics Data System (ADS)
Santos, E. S.; de Montigny, M.; Khanna, F. C.
2005-11-01
The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein-Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term λΦ4. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron-electron and the electron-positron scattering. These examples show that the so-called 'non-relativistic' approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.
Homotopy Classification of Bosonic String Field Theory
NASA Astrophysics Data System (ADS)
Münster, Korbinian; Sachs, Ivo
2014-09-01
We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.
Towards weakly constrained double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2016-08-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Multiscale quantum simulation of quantum field theory using wavelets
NASA Astrophysics Data System (ADS)
Brennen, Gavin K.; Rohde, Peter; Sanders, Barry C.; Singh, Sukhwinder
2015-09-01
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis—a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.
Gauge anomalies in an effective field theory
Preskill, J. )
1991-09-01
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Logarithmic operators and logarithmic conformal field theories
NASA Astrophysics Data System (ADS)
Gurarie, Victor
2013-12-01
Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c = -2 and c = 0 logarithmic conformal field theories. c = 0 logarithmic conformal field theories are especially interesting since they describe some of the critical points of a variety of longstanding problems involving a two dimensional quantum particle moving in a spatially random potential, as well as critical two dimensional self-avoiding random walks and percolation. Lack of classification of logarithmic conformal field theories remains a major impediment to progress towards finding complete solutions to these problems.
Remnant group of local Lorentz transformations in f (T ) theories
NASA Astrophysics Data System (ADS)
Ferraro, Rafael; Fiorini, Franco
2015-03-01
It is shown that the extended teleparallel gravitational theories, known as f (T ) theories, inherit some on shell local Lorentz invariance associated with the tetrad field defining the spacetime structure. We discuss some enlightening examples, such as Minkowski spacetime and cosmological (Friedmann-Robertson-Walker and Bianchi type I) manifolds. In the first case, we show that the absence of gravity reveals itself as an incapability in the selection of a preferred parallelization at a local level, due to the fact that the infinitesimal local Lorentz subgroup acts as a symmetry group of the frame characterizing Minkowski spacetime. Finite transformations are also discussed in these examples and, contrary to the common lore on the subject, we conclude that the set of tetrads responsible for the parallelization of these manifolds is quite vast and that the remnant group of local Lorentz transformations includes one- and two-dimensional Abelian subgroups of the Lorentz group.
Spectral renormalization group theory on nonspatial networks
NASA Astrophysics Data System (ADS)
Tuncer, Asli; Erzan, Ayse
We recently proposed a ``spectral renormalization group'' scheme, for non-spatial networks with no metric defined on them. We implemented the spectral renormalization group on two deterministic non-spatial networks without translational invariance, namely the Cayley tree and diamond lattice . The thermodynamic critical exponents for the Gaussian model are only functions of the spectral dimension, d ~. The Gaussian fixed point is stable with respect to a Ψ4 perturbation up to second order on these lattices with d ~ = 2 , the lower critical dimension for the Ising universality class. This is expected for the Cayley tree, but for the diamond lattice it is an indication that the perturbation expansion up to second order breaks down at d ~ = 2 , as it does for the Wilson scheme on the square lattice. On generalized diamond lattices, with 2 < d ~ < 4 , we find non-Gaussian fixed points with non-trivial exponents. For d ~ > 4 , the critical behavior is once again mean field.
Renormalization group evolution of the universal theories EFT
NASA Astrophysics Data System (ADS)
Wells, James D.; Zhang, Zhengkang
2016-06-01
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.
String theory, supergravity and four-dimensional field theories
NASA Astrophysics Data System (ADS)
Burrington, Benjamin A.
of these superpartners and use this to determine the representation of the AdS5 superalgebra that these black holes belong to. In chapter 7 and 8 we turn to the field theory side of AdS/CFT. Here, we consider certain discrete symmetries of these field theories. The discrete symmetries are dual to the number operators for certain wrapped branes. We find that the generators for these discrete symmetries do not commute. This feature of wrapped branes was uncovered in the literature for the field theory dual to S5/Z3 . In addition to generalizing this to certain classes of Yp,q geometries in chapter 7, we also find that the non conformal case admits a centrally extended Heisenberg group structure in chapter 8.
An extremal ${\\mathcal{N}}=2$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiral ${\\mathcal{N}}$ = 2 superconformal field theory at c = 24. The construction is based on a ${{\\mathbb{Z}}}_{2}$ orbifold of the theory associated to the ${A}_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.
An extremal $${\\mathcal{N}}=2$$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiralmore » $${\\mathcal{N}}$$ = 2 superconformal field theory at c = 24. The construction is based on a $${{\\mathbb{Z}}}_{2}$$ orbifold of the theory associated to the $${A}_{1}^{24}$$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.« less
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
Three approaches to classical thermal field theory
NASA Astrophysics Data System (ADS)
Gozzi, E.; Penco, R.
2011-04-01
In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Descent relations in cubic superstring field theory
NASA Astrophysics Data System (ADS)
Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.
2008-01-01
The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations langleV2|V1rangle and langleV3|V1rangle in the NS fermionic string field theory in the κ and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
Conformal field theories, representations and lattice constructions
NASA Astrophysics Data System (ADS)
Dolan, L.; Goddard, P.; Montague, P.
1996-07-01
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z 2-twisted theories, ℋ( Λ) andtilde H(Λ ) respectively, which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct latticesΛ _C andtilde Λ _C by analogous constructions from a doubly-even binary codeC. In the case whenC is self-dual, the corresponding lattices are also. Similarly, ℋ( Λ) andtilde H(Λ ) are self-dual if and only if Λ is. We show thatH(Λ _C ) has a natural “triality” structure, which induces an isomorphismH(tilde Λ _C ) ≡tilde H(Λ _C ) and also a triality structure ontilde H(tilde Λ _C ). ForC the Golay code,tilde Λ _C is the Leech lattice, and the triality ontilde H(tilde Λ _C ) is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories ℋ( Λ) andtilde H(Λ ) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.
E11 and exceptional field theory
NASA Astrophysics Data System (ADS)
Tumanov, Alexander G.; West, Peter
2016-04-01
We argue that the exceptional field theory is a truncation of the nonlinear realisation of the semi-direct product of E11 and its first fundamental as proposed in 2003. Evaluating the simple equations of the E11 approach, and using the commutators of the E11 algebra, we find the local variations of the fields of exceptional field theory after making a radical truncation. This procedure does not respect any of the higher level E11 symmetries and so these are lost. We suggest that the need for the section condition in the exceptional field theory could be a consequence of the truncation.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2010-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
Standard Model as a Double Field Theory.
Choi, Kang-Sin; Park, Jeong-Hyuck
2015-10-23
We show that, without any extra physical degree introduced, the standard model can be readily reformulated as a double field theory. Consequently, the standard model can couple to an arbitrary stringy gravitational background in an O(4,4) T-duality covariant manner and manifest two independent local Lorentz symmetries, Spin(1,3)×Spin(3,1). While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the standard model more rigid, and also stringy, than it appeared. The CP violating θ term may no longer be allowed by the symmetry, and hence the strong CP problem can be solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may belong to the two different spin classes. PMID:26551099
Standard Model as a Double Field Theory
NASA Astrophysics Data System (ADS)
Choi, Kang-Sin; Park, Jeong-Hyuck
2015-10-01
We show that, without any extra physical degree introduced, the standard model can be readily reformulated as a double field theory. Consequently, the standard model can couple to an arbitrary stringy gravitational background in an O (4 ,4 ) T -duality covariant manner and manifest two independent local Lorentz symmetries, Spin(1 ,3 )×Spin(3 ,1 ) . While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the standard model more rigid, and also stringy, than it appeared. The C P violating θ term may no longer be allowed by the symmetry, and hence the strong C P problem can be solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may belong to the two different spin classes.
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
Marginally Relevant Topics in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Cleary, Kevin Francis
We consider a set of topics in conformal field theory. We provide an example of a 4D theory that exhibits the Contino-Pomarol-Rattazzi mechanism, where breaking conformal symmetry by an almost marginal operator leads to a light pseudo-Goldstone boson, the dilaton, and a parametrically suppressed contribution to vacuum energy. We consider SUSY QCD at the edge of the conformal window and break conformal symmetry by weakly gauging a subgroup of the flavor symmetry. Using Seiberg duality we show that for a range of parameters the singlet meson in the dual theory reaches the unitarity bound, however, this theory does not have a stable vacuum. We stabilize the vacuum with soft breaking terms, compute the mass of the dilaton, and determine the range of parameters where the leading contribution to the dilaton mass is from the almost marginal coupling. We also weigh in on a widely held belief that increasing bounds on the gluino mass, which feeds down to the stop mass through renormalization group running, are making a light stop increasingly unlikely. Here we present a counter-example. We examine the case of the Minimal Composite Supersymmetric Standard Model which has a light composite stop. The large anomalous dimension of the stop from strong dynamics pushes the stop mass toward a quasi-fixed point in the infrared, which is smaller than standard estimates by a factor of a large logarithm. The gluino can be about three times heavier than the stop, which is comparable to hierarchy achieved with supersoft Dirac gluino masses. Thus, in this class of models, a heavy gluino is not necessarily indicative of a heavy stop.
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Holographic renormalization group and cosmology in theories with quasilocalized gravity
NASA Astrophysics Data System (ADS)
Csáki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-01
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
Holographic renormalization group and cosmology in theories with quasilocalized gravity
Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-15
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Ring, Peter; Zhao, Pengwei
In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.
A nonlinear field theory of deformable dielectrics
NASA Astrophysics Data System (ADS)
Suo, Zhigang; Zhao, Xuanhe; Greene, William H.
Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.
Quantum statistical correlations in thermal field theories: Boundary effective theory
Bessa, A.; Brandt, F. T.; Carvalho, C. A. A. de; Fraga, E. S.
2010-09-15
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field {phi}{sub c}, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schroedinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field {phi}{sub c}, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Attachment to groups: theory and measurement.
Smith, E R; Murphy, J; Coats, S
1999-07-01
Aspects of people's identification with groups may be understood by borrowing theoretical ideas and measurement strategies from research on attachment in close relationships. People have mental models of the self as a group member and of groups as sources of identity and esteem. These models affect thoughts, emotions, and behaviors related to group membership. Three studies show that two dimensions of attachment to groups, attachment anxiety and avoidance, can be assessed with good reliability, validity, and over-time stability. These factors are distinct from relationship attachment and from other measures of group identification. Group attachment predicts several important outcomes, including emotions concerning the group, time and activities shared with a group, social support, collective self-esteem, and ways of resolving conflict. This conceptualization provides new insights into the nature of people's psychological ties to groups. PMID:10434410
Weyl's Abandonment of Unified Field Theory
NASA Astrophysics Data System (ADS)
Sieroka, Norman
2015-01-01
In 1918, Hermann Weyl proposed a generalisation of Riemannian geometry, in order to unify general relativity and electrodynamics. This paper investigates the physical, mathematical and philosophical reasons for his subsequent abandonment of any such attempt towards a unified field theory.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
Small Group Learning: Do Group Members' Implicit Theories of Ability Make a Difference?
ERIC Educational Resources Information Center
Beckmann, Nadin; Wood, Robert E.; Minbashian, Amirali; Tabernero, Carmen
2012-01-01
We examined the impact of members' implicit theories of ability on group learning and the mediating role of several group process variables, such as goal-setting, effort attributions, and efficacy beliefs. Comparisons were between 15 groups with a strong incremental view on ability (high incremental theory groups), and 15 groups with a weak…
Better Field Instruction by Using Jigsaw Groups
NASA Astrophysics Data System (ADS)
Sammons, J. I.; Murray, D. P.
2006-12-01
Do any of these sound familiar? Most of my students do well at field stops, but there are always the few at the back. I'd like to guest speak at the local High School, but the students have too little background. I wish I could spark the interest of my introductory classes. Jigsaw is the solution to these problems. This easy-to-apply technique puts students in the driver's seat. They make the inferences-they own the discovery. You'll see that "A-ha!" as though it were a first time event. Jigsaw brings new excitement to familiar activities for every student in your class, even that guy in the back. Best of all, the technique does not depend on the style or force of personality of the instructor. It is easy to learn and suitable for use by Teaching Assistants. Here's how it works: 1. Identify the critical concepts necessary for a full understanding of the field stop or activity. 2. Divide your class into Expert Groups. The members of each Expert Group will master one of these critical concepts. 3.Dissolve the Expert Groups. Divide your class into new Jigsaw Groups to address the field stop or activity. Each Jigsaw Group includes members from each Expert Group. Like pieces of a puzzle, each Jigsaw Group member brings a critical piece to the problem. This talk will demonstrate Jigsaw Groups in action at a field stop. You'll see the crucial identification of critical concepts, small lab explorations carried out by the Expert Groups to master their assigned concepts, and Jigsaw Groups working a complex geological feature. You'll learn how to trouble-shoot less-than-successful first attempts and you'll leave with a step-by-step template that will allow you to adapt your existing activities to Jigsaw technique.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Reductionism, emergence, and effective field theories
NASA Astrophysics Data System (ADS)
Castellani, Elena
In recent years, a "change in attitude" in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
Conserved currents of double field theory
NASA Astrophysics Data System (ADS)
Blair, Chris D. A.
2016-04-01
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.
New class of effective field theories from embedded branes.
Goon, Garrett L; Hinterbichler, Kurt; Trodden, Mark
2011-06-10
We present a new general class of four-dimensional effective field theories with interesting global symmetry groups. These theories arise from purely gravitational actions for (3+1)-dimensional branes embedded in higher dimensional spaces with induced gravity terms. The simplest example is the well known Galileon theory, with its associated Galilean symmetry, arising as the limit of a DGP brane world. However, we demonstrate that this is a special case of a much wider range of theories, with varying structures, but with the same attractive features such as second order equations. In some circumstances, these new effective field theories allow potentials for the scalar fields on curved space, with small masses protected by nonlinear symmetries. Such models may prove relevant to the cosmology of both the early and late universe. PMID:21770494
Bound states in gauge theories as the Poincare group representations
Cherny, A. Yu.; Dorokhov, A. E.; Han, Nguyen Suan; Pervushin, V. N. Shilin, V. I.
2013-03-15
The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincare group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of {gamma} + {gamma} {yields} {pi}{sub 0} +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.
Effective field theory out of equilibrium: Brownian quantum fields
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-06-01
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
THE VELOCITY FIELD AROUND GROUPS OF GALAXIES
Hartwick, F. D. A.
2011-06-15
A statistical method is presented for determining the velocity field in the immediate vicinity of groups of galaxies using only positional and redshift information with the goal of studying the perturbation of the Hubble flow around groups more distant than the Local Group. The velocities are assumed to obey a Hubble-like expansion law, i.e., V = H{sub exp} R, where the expansion rate H{sub exp} is to be determined. The method is applied to a large, representative group catalog and evidence is found for a sub-Hubble expansion rate within two well-defined radii beyond the virial radii of the groups. This result is consistent with that of Teerikorpi et al. who found a similar expansion law around three nearby groups and extends it to a more representative volume of space.
Hamiltonian constraint in polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2011-01-15
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
New symbolic tools for differential geometry, gravitation, and field theory
NASA Astrophysics Data System (ADS)
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
Dynamical theory of dense groups of galaxies
NASA Technical Reports Server (NTRS)
Mamon, Gary A.
1990-01-01
It is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups.
Far-field environment working group summary
Pearcy, E.C.; Cady, R.E.
1995-09-01
This article is a summary of the proceedings of a group discussion which took place at the Workshop on the Role of Natural Analogs in Geologic Disposal of High-Level Nuclear Waste in San Antonio, Texas on July 22-25, 1991. The working group concentrated on the subject of the potential impacts of underground disposal of high-level radioactive wastes on the far-field environment.
Entanglement entropy in warped conformal field theories
NASA Astrophysics Data System (ADS)
Castro, Alejandra; Hofman, Diego M.; Iqbal, Nabil
2016-02-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL (2, ℝ) × U (1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
Optomechanical shape analysis using group theory.
Magnes, Jenny; Kinneberg, Margo; Khakurel, Rahul; Melikechi, Noureddine
2010-08-01
We describe an optomechanical technique using a knife-edge, which is scanned spatially across a beam of light to identify shape-based irradiance. Symmetry groups are identified through linear and rotational scanning signatures of illuminated shapes. The scanning signature is used to classify the shape into a symmetry group. To demonstrate the shape analysis technique, we have classified basic geometric shapes, which belong to the orthogonal and dihedral symmetry groups O(2), D(2), D(3), and D(6). PMID:20676172
Hunton Group core workshop and field trip
Johnson, K.S.
1993-12-31
The Late Ordovician-Silurian-Devonian Hunton Group is a moderately thick sequence of shallow-marine carbonates deposited on the south edge of the North American craton. This rock unit is a major target for petroleum exploration and reservoir development in the southern Midcontinent. The workshop described here was held to display cores, outcrop samples, and other reservoir-characterization studies of the Hunton Group and equivalent strata throughout the region. A field trip was organized to complement the workshop by allowing examination of excellent outcrops of the Hunton Group of the Arbuckle Mountains.
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Recursive renormalization group theory based subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE
1991-01-01
Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory
NASA Astrophysics Data System (ADS)
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010), 10.1103/PhysRevE.81.061102; J. Stat. Phys. 149, 643 (2012), 10.1007/s10955-012-0610-y; J. Stat. Phys. 152, 159 (2013), 10.1007/s10955-013-0755-3; Phys. Rev. E 83, 041125 (2011), 10.1103/PhysRevE.83.041125] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Effective Field Theories, Reductionism and Scientific Explanation
NASA Astrophysics Data System (ADS)
Hartmann, Stephan
Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation.
The field theory of intersecting D3-branes
NASA Astrophysics Data System (ADS)
Mintun, Eric; Polchinski, Joseph; Sun, Sichun
2015-08-01
We examine the defect gauge theory on two perpendicular D3-branes with a 1+1 dimensional intersection, consisting of U(1) fields on the D3-branes and charged hypermultiplets on the intersection. We argue that this gauge theory must have a magnetically charged soliton corresponding to the D-string stretched between the branes. We show that the hypermultiplets actually source magnetic as well as electric fields. The magnetic charges are confined if the hypermultiplet action is canonical, but considerations of periodicity of the hypermultiplet space in string theory imply a nontrivial Gibbons-Hawking metric, and we show that there is then the expected magnetic kink solution. The hypermultiplet metric has a singularity, which we argue must be resolved by embedding in the full string theory. Another interesting feature is that the classical field equations have logarithmic divergences at the intersection, which lead to a classical renormalization group flow in the action.
Quantum Cylindrical Waves and Parametrized Field Theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space-time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space-time and review the relevant results for unitary implementability.
Working group on chromospheric fields - Canopies
NASA Technical Reports Server (NTRS)
Jones, H. P.
1985-01-01
Although there are many points of uncertainty and controversy, the working group on chromospheric fields focussed its discussion on the concept of canopies; i.e., no one disagreed that a central issue relating to magnetic fields and chromospheric models is to learn how the photospheric field spreads with height. However, it quickly became apparent that in the time available, there was little prospect of building new unified models of magnetic field phenomena in the chromosphere beyond the scope of the formal presentations. Thus, the discussion was devoted to formulating questions which seemed both possible to address in future work and important for advancing understanding of the chromosphere. It began by discussing unresolved physical issues (almost everything) and then proceeded to consider means, both observational and synthetic, to address them.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
Non Perturbative Aspects of Field Theory
Bashir, A.
2009-04-20
For any quantum field theory (QFT), there exists a set of Schwinger-Dyson equations (SDE) for all its Green functions. However, it is not always straight forward to extract quantitatively exact physical information from this set of equations, especially in the non perturbative regime. The situation becomes increasingly complex with growing number of external legs. I give a qualitative account of the hunt for the non perturbative Green functions in gauge theories.
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Electroweak Sudakov Corrections using Effective Field Theory
Chiu Juiyu; Golf, Frank; Kelley, Randall; Manohar, Aneesh V.
2008-01-18
Electroweak Sudakov corrections of the form {alpha}{sup n}log{sup m}s/M{sub W,Z}{sup 2} are summed using renormalization group evolution in soft-collinear effective theory. Results are given for the scalar, vector, and tensor form factors for fermion and scalar particles. The formalism for including massive gauge bosons in soft-collinear effective theory is developed.
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
The Real K-Theory of Compact Lie Groups
NASA Astrophysics Data System (ADS)
Fok, Chi-Kwong
2014-03-01
Let G be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution σ_G and viewed as a G-space with the conjugation action. In this paper, we present a description of the ring structure of the (equivariant) KR-theory of (G, σ_G) by drawing on previous results on the module structure of the KR-theory and the ring structure of the equivariant K-theory.
Not Available
1992-01-01
The effort of the experimental group has been concentrated on the CERN ALEPH and FERMILAB D0 collider experiments and completion of two fixed target experiments. The BNL fixed target experiment 771 took the world's largest sample of D(1285) and E/iota(1420) events, using pion, kaon and antiproton beams. Observing the following resonances: 0[sup [minus plus
Global anomalies and effective field theory
NASA Astrophysics Data System (ADS)
Golkar, Siavash; Sethi, Savdeep
2016-05-01
We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on thermal effective field theory, where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient (up to an overall additive factor). This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Social Learning Theory and Group Behavioral Change.
ERIC Educational Resources Information Center
Turner, David; Balow, Bruce
This study investigated whether collaborative and socially sensitive behaviors, necessary in group problem solving, can be taught to emotionally disturbed children in residential treatment centers. The sample consisted of 180 males ranging in age from nine through 12 years in 12 residential centers. The children were required to perform a…
Generalized conservation laws in non-local field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Cluster Mass Inference via Random Field Theory
Zhang, Hui; Nichols, Thomas E.; Johnson, Timothy D.
2009-01-01
Cluster extent and voxel intensity are two widely used statistics in neuroimaging inference. Cluster extent is sensitive to spatially extended signals while voxel intensity is better for intense but focal signals. In order to leverage strength from both statistics, several nonparametric permutation methods have been proposed to combine the two methods. Simulation studies have shown that of the different cluster permutation methods, the cluster mass statistic is generally the best. However, to date, there is no parametric cluster mass inference method available. In this paper, we propose a cluster mass inference method based on random field theory (RFT). We develop this method for Gaussian images, evaluate it on Gaussian and Gaussianized t-statistic images and investigate its statistical properties via simulation studies and real data. Simulation results show that the method is valid under the null hypothesis and demonstrate that it can be more powerful than the cluster extent inference method. Further, analyses with a single-subject and a group fMRI dataset demonstrate better power than traditional cluster extent inference, and good accuracy relative to a gold-standard permutation test. PMID:18805493
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
On the History of Unified Field Theories
NASA Astrophysics Data System (ADS)
Goenner, Hubert F. M.
2004-02-01
This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin - with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger's or Dirac's equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopocraphical remarks are included.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Generalization of trinification to theories with 3N SU(3) gauge groups
Carone, Christopher D.
2005-04-01
We consider a natural generalization of trinification to theories with 3N SU(3) gauge groups. These theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5D theory with unified symmetry broken on a boundary. Although the matter and Higgs sectors of the theory have no simple extra-dimensional analog, gauge unification retains features characteristic of the 5D theory. We determine possible assignments of the matter and Higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified GUTs.
The Mean-Field Flux Pinning Theory
NASA Astrophysics Data System (ADS)
Stejic, George
We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Double field theory: a pedagogical review
NASA Astrophysics Data System (ADS)
Aldazabal, Gerardo; Marqués, Diego; Núñez, Carmen
2013-08-01
Double field theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions and present a brief parcours on worldsheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.
Causality constraints in conformal field theory
NASA Astrophysics Data System (ADS)
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Effective Field Theory in Nuclear Astrophysics
NASA Astrophysics Data System (ADS)
Chen, Jiunn-Wei
2001-04-01
I will discuss some basic ideas of effective field theory and its application to two nucleon systems. The theory allows a perturbative treatment of strongly interacting, bound state problems such that the calculations can be systematically improved and reliable error estimation performed. Also, the field theory formalism naturally allows manifest incorporation of symmetry properties such as gauge symmetry and Lorentz symmetry. Emphasis will be placed on some high precision calculations to low energy astrophysical problems: neutron radiative capture onto proton which is relevant to big-bang nucleosynthesis; neutrino deuteron inelastic scattering employed in the solar neutrino detection by Sudbury Neutrino Observatory (SNO) and the proton-proton solar fusion process which is an important process to fuel the sun. The last two classes of processes share the same two-body operator which is proposed to be measured at ORLAND and could serve to calibrate SNO and the solar fusion rate.
Global effects in quaternionic quantum field theory
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.
1996-12-01
We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and nonbaryonic hot dark matter candidates.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
Prequantum Classical Statistical Field Theory: Fundamentals
Khrennikov, Andrei
2011-03-28
We present fundamentals of a prequantum model with hidden variables of the classical field type. In some sense this is the comeback of classical wave mechanics. Our approach also can be considered as incorporation of quantum mechanics into classical signal theory. All quantum averages (including correlations of entangled systems) can be represented as classical signal averages and correlations.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Group-kinetic theory of turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.
Thermodynamics of perfect fluids from scalar field theory
NASA Astrophysics Data System (ADS)
Ballesteros, Guillermo; Comelli, Denis; Pilo, Luigi
2016-07-01
The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of Stückelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the thermodynamic variables, we find that a complete thermodynamic picture requires the four Stückelberg fields. We show that thermodynamic stability plus the null-energy condition imply dynamical stability. We also argue that a consistent thermodynamic interpretation is not possible if any of the shift symmetries is explicitly broken.
Quantum stability of chameleon field theories.
Upadhye, Amol; Hu, Wayne; Khoury, Justin
2012-07-27
Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m<0.0073(ρ/10 g cm(-3))(1/3) eV for gravitational-strength coupling whereas fifth force experiments place a lower bound of m>0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073
A computational theory of visual receptive fields.
Lindeberg, Tony
2013-12-01
A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative
Quantization of non-local field theory and string field theory
NASA Astrophysics Data System (ADS)
Hata, Hiroyuki
1989-02-01
The interaction vertex in covariant string field theory (SFT) is non-local in the time coordinate and the conventional canonical quantization is inapplicable to it. As an approach to quantizing this system we apply Hayashi's theory of the Hamilton formalism for field theories with non-local interactions. We find that the resulting one-loop amplitudes in covariant closed SFT coincide with those in the light-cone gauge SFT. I would like to thank T. Kugo, H. Kunitomo, M.M. Nojiri, K. Ogawa and K. Suehiro for valuable discussions, and especially Professor S. Tanaka for directing my attention to Hayashi's theory.
Reading Discussion Groups for Teachers: Connecting Theory to Practice
ERIC Educational Resources Information Center
Fenton-Smith, Ben; Stillwell, Christopher
2011-01-01
This article explores how teachers can engage with ideas (research findings, theory, and professional knowledge) through participation in a reading discussion group. Focusing on one group formed by English language teachers at a Japanese university, the study employs survey data, attendance statistics, and observational notes regarding the group's…
Using Group Development Theory in Business and Industry.
ERIC Educational Resources Information Center
Kormanski, Chuck
1988-01-01
Examines and compares theories of group development using a historical perspective, and presents a summary of the models of group development and their sequential stages. Identifies five trends in business and industry that characterize the group process: those relating to management style, need levels, transactional and transformational skills,…
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Marginal deformations of nonrelativistic field theories
NASA Astrophysics Data System (ADS)
Mallayev, Davron; Vázquez-Poritz, Justin F.; Zhang, Zhibai
2014-11-01
We construct the supergravity duals of marginal deformations of a (0, 2) Landau-Ginsburg theory that describes the supersymmetric lowest Landau level. These deformations preserve supersymmetry and it is proposed that they are associated with the introduction of a phase in the (0, 2) superpotential. We also consider marginal deformations of various field theories that exhibit Schrödinger symmetry and Lifshitz scaling. This includes countably infinite examples with dynamical exponent z =2 based on the Sasaki-Einstein spaces Yp ,q and Lp ,q ,r, as well as an example with general dynamical exponent z ≥1 .
Bayesian parameter estimation for effective field theories
NASA Astrophysics Data System (ADS)
Wesolowski, Sarah; Klco, Natalie; Furnstahl, Richard; Phillips, Daniel; Thapilaya, Arbin
2015-10-01
We present a procedure based on Bayesian statistics for effective field theory (EFT) parameter estimation from experimental or lattice data. The extraction of low-energy constants (LECs) is guided by physical principles such as naturalness in a quantifiable way and various sources of uncertainty are included by the specification of Bayesian priors. Special issues for EFT parameter estimation are demonstrated using representative model problems, and a set of diagnostics is developed to isolate and resolve these issues. We apply the framework to the extraction of the LECs of the nucleon mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Magnetic fields in Local Group dwarf irregulars
NASA Astrophysics Data System (ADS)
Chyży, K. T.; Weżgowiec, M.; Beck, R.; Bomans, D. J.
2011-05-01
Aims: We wish to clarify whether strong magnetic fields can be effectively generated in typically low-mass dwarf galaxies and to assess the role of dwarf galaxies in the magnetization of the Universe. Methods: We performed a search for radio emission and magnetic fields in an unbiased sample of 12 Local Group (LG) irregular and dwarf irregular galaxies with the 100-m Effelsberg telescope at 2.64 GHz. Three galaxies were detected. A higher frequency (4.85 GHz) was used to search for polarized emission in five dwarfs that are the most luminous ones in the infrared domain, of which three were detected. Results: Magnetic fields in LG dwarfs are weak, with a mean value of the total field strength of <4.2 ± 1.8 μG, three times lower than in the normal spirals. The strongest field among all LG dwarfs of 10 μG (at 2.64 GHz) is observed in the starburst dwarf IC 10. The production of total magnetic fields in dwarf systems appears to be regulated mainly by the star-formation surface density (with the power-law exponent of 0.30 ± 0.04) or by the gas surface density (with the exponent 0.47 ± 0.09). In addition, we find systematically stronger fields in objects of higher global star-formation rate. The dwarf galaxies follow a similar far-infrared relationship (with a slope of 0.91 ± 0.08) to that determined for high surface brightness spiral galaxies. The magnetic field strength in dwarf galaxies does not correlate with their maximum rotational velocity, indicating that a small-scale rather than a large-scale dynamo process is responsible for producting magnetic fields in dwarfs. If magnetization of the Universe by galactic outflows is coeval with its metal enrichment, we show that more massive objects (such as Lyman break galaxies) can efficiently magnetize the intergalactic medium with a magnetic field strength of about 0.8 nG out to a distance of 160-530 kpc at redshifts 5-3, respectively. Magnetic fields that are several times weaker and shorter magnetization
Group-III Nitride Field Emitters
NASA Technical Reports Server (NTRS)
Bensaoula, Abdelhak; Berishev, Igor
2008-01-01
Field-emission devices (cold cathodes) having low electron affinities can be fabricated through lattice-mismatched epitaxial growth of nitrides of elements from group III of the periodic table. Field emission of electrons from solid surfaces is typically utilized in vacuum microelectronic devices, including some display devices. The present field-emission devices and the method of fabricating them were developed to satisfy needs to reduce the cost of fabricating field emitters, make them compatible with established techniques for deposition of and on silicon, and enable monolithic integration of field emitters with silicon-based driving circuitry. In fabricating a device of this type, one deposits a nitride of one or more group-III elements on a substrate of (111) silicon or other suitable material. One example of a suitable deposition process is chemical vapor deposition in a reactor that contains plasma generated by use of electron cyclotron resonance. Under properly chosen growth conditions, the large mismatch between the crystal lattices of the substrate and the nitride causes strains to accumulate in the growing nitride film, such that the associated stresses cause the film to crack. The cracks lie in planes parallel to the direction of growth, so that the growing nitride film becomes divided into microscopic growing single-crystal columns. The outer ends of the fully-grown columns can serve as field-emission tips. By virtue of their chemical compositions and crystalline structures, the columns have low work functions and high electrical conductivities, both of which are desirable for field emission of electrons. From examination of transmission electron micrographs of a prototype device, the average column width was determined to be about 100 nm and the sharpness of the tips was determined to be characterized by a dimension somewhat less than 100 nm. The areal density of the columns was found to about 5 x 10(exp 9)/sq cm . about 4 to 5 orders of magnitude
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
A Grounded Theory of Western-Trained Asian Group Leaders Leading Groups in Asia
ERIC Educational Resources Information Center
Taephant, Nattasuda; Rubel, Deborah; Champe, Julia
2015-01-01
This grounded theory research explored the experiences of Western-trained Asian group leaders leading groups in Asia. A total of 6 participants from Japan, Taiwan, and Thailand were interviewed 3 times over 9 months. The recursive process of data collection and analysis yielded substantive theory describing the participants' process of…
An Intuitive Approach to Group Representation Theory, II.
ERIC Educational Resources Information Center
Wolbarst, A. B.
1979-01-01
This is the second of several papers which attempts to introduce group representation theory to students of molecular or solid-state physics in as intuitive and simple a fashion as possible. (Author/BB)
Theory of gain in group-III nitride lasers
Chow, W.W.; Wright, A.F.; Girndt, A.
1997-06-01
A microscopic theory of gain in a group-III nitride quantum well laser is presented. The approach, which treats carrier correlations at the level of quantum kinetic theory, gives a consistent account of plasma and excitonic effects in an inhomogeneously broadened system.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Twistor Diagrams and Quantum Field Theory.
NASA Astrophysics Data System (ADS)
O'Donald, Lewis
Available from UMI in association with The British Library. Requires signed TDF. This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical view-point, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, 1990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sum-over -states idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various massless propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman "fish" diagrams of phi^4 -theory. However it is found that a more rigorous translation for the time-like fish requires new boundaries to be added to the twistor sum-over-states. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.
Radiative reactions in halo effective field theory
NASA Astrophysics Data System (ADS)
Rupak, Gautam
2016-03-01
In this article we review the recent progress in radiative reaction calculations in halo effective field theory. We look at radiative capture and breakup processes that involve a halo nucleus with a single valence neutron or proton. Looking at 7Li(n,γ) 8Li,14C(n,γ)15C and related reactions, the dominant source of theoretical uncertainty in s- and p-wave halo nuclei reaction calculations is quantified in a model-independent framework. The analysis for neutron halos is extended to proton halo systems. The effective field theory results quantify which observable parameters of the strong interaction at low energy need to be determined more precisely for accurate cross-section calculations.
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Quantum algorithms for quantum field theories
NASA Astrophysics Data System (ADS)
Jordan, Stephen
2015-03-01
Ever since Feynman's original proposal for quantum computers, one of the primary applications envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that quantum computers would be universal simulators, which can simulate all physical systems using computational resources that scale polynomially with the system's number of degrees of freedom. Quantum field theories have posed a challenge in that the set of degrees of freedom is formally infinite. We show how quantum computers, if built, could nevertheless efficiently simulate certain quantum field theories at bounded energy scales. Our algorithm includes a new state preparation technique which we believe may find additional applications in quantum algorithms. Joint work with Keith Lee and John Preskill.
Effective Field Theory for Lattice Nuclei
NASA Astrophysics Data System (ADS)
Barnea, N.; Contessi, L.; Gazit, D.; Pederiva, F.; van Kolck, U.
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at mπ≈800 MeV , we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states.
Effective field theory for lattice nuclei.
Barnea, N; Contessi, L; Gazit, D; Pederiva, F; van Kolck, U
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at m_{π}≈800 MeV, we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states. PMID:25699436
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Entanglement entropy in scalar field theory
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.
2013-01-01
Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here we perturbatively calculate the entanglement entropy in interacting scalar field theory, focusing on the dependence on the field’s mass. We study λϕ4 and gϕ3 theories in their ground state. By tracing over a half space, using the replica trick and position space Green’s functions on the cone, we show that spacetime volume divergences cancel and renormalization can be consistently performed in this conical geometry. We establish finite contributions to the entanglement entropy up to two-loop order, involving a finite area law. The resulting entropy is simple and intuitive: the free theory result in d = 3 (that we included in an earlier publication) ΔS ˜ A m2ln (m2) is altered, to leading order, by replacing the bare mass m by the renormalized mass mr evaluated at the renormalization scale of zero momentum.
Complete action for open superstring field theory
NASA Astrophysics Data System (ADS)
Kunitomo, Hiroshi; Okawa, Yuji
2016-02-01
We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is invariant under gauge transformations that are consistent with the projection for the string field in the Ramond sector.
Higher spin double field theory: a proposal
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Park, Jeong-Hyuck
2016-07-01
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Capture Reactions with Halo Effective Field Theory
NASA Astrophysics Data System (ADS)
Higa, R.
2015-12-01
Loosely bound nuclei far from the stability region emerge as a quantum phenomenon with many universal properties. The connection between these properties and the underlying symmetries can be best explored with halo/cluster EFT, an effective field theory where the softness of the binding momentum and the hardness of the core(s) form the expansion parameter of a given perturbative approach. In the following I highlight a particular application where these ideas are being tested, namely capture reactions.
Halo Effective Field Theory of 6He
NASA Astrophysics Data System (ADS)
Thapaliya, Arbin; Ji, Chen; Phillips, Daniel
2016-03-01
6He has a cluster structure with a tight 4He (α) core surrounded by two loosely bound neutrons (n) making it a halo nucleus. The leading-order (LO) Halo Effective Field Theory (EFT) [1, 2] calculations using momentum-space Faddeev equations pertinent to a bound 6He were carried out in [3]. In this work, we investigate 6He up to next-to-leading order (NLO) within Halo EFT.
Closed string field theory from polyhedra
NASA Astrophysics Data System (ADS)
Saadi, Maha; Zwiebach, Barton
1989-05-01
A fully nonpolynomial framework for closed string field theory is studied. All interactions are geometrical, the pattern of string overlaps gives polyhedra with equal perimeter faces and three edges at each vertex. All interactions are cubic in the sense that at most three strings can coincide at a point. The three point vertex used is that of Witten which is seen to be quite natural in the framework of quadratic differentials and to induce a very symmetric decomposition of moduli space.
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
NASA Astrophysics Data System (ADS)
Schenkel, Alexander
2012-10-01
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that these theories have an improved behaviour at short distances, i.e. in the ultraviolet. In part three we study homomorphisms between and connections on noncommutative vector bundles. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of bimodules is clarified. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.
Backreacted axion field ranges in string theory
NASA Astrophysics Data System (ADS)
Baume, Florent; Palti, Eran
2016-08-01
String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter controlling the effective decay constant is unconstrained by tadpoles and can in principle lead to an arbitrarily large effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement leaving a sub-Planckian effective decay constant.
Capturing the superorganism: a formal theory of group adaptation.
Gardner, A; Grafen, A
2009-04-01
Adaptation is conventionally regarded as occurring at the level of the individual organism. However, in recent years there has been a revival of interest in the possibility for group adaptations and superorganisms. Here, we provide the first formal theory of group adaptation. In particular: (1) we clarify the distinction between group selection and group adaptation, framing the former in terms of gene frequency change and the latter in terms of optimization; (2) we capture the superorganism in the form of a 'group as maximizing agent' analogy that links an optimization program to a model of a group-structured population; (3) we demonstrate that between-group selection can lead to group adaptation, but only in rather special circumstances; (4) we provide formal support for the view that between-group selection is the best definition for 'group selection'; and (5) we reveal that mechanisms of conflict resolution such as policing cannot be regarded as group adaptations. PMID:19210588
Unexpected connections between Burnside groups and knot theory.
Dabkowski, Mieczyslaw K; Przytycki, Józef H
2004-12-14
In classical knot theory and the theory of quantum invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this article, several classical problems concerning unknotting moves. Our approach uses a concept, Burnside groups of links, that establishes an unexpected relationship between knot theory and group theory. Our method has the potential to be used in computational biology in the analysis of DNA via tangle embedding theory, as developed by D. W. Sumners [Sumners, D. W., ed. (1992) New Scientific Applications of Geometry and Topology (Am Math. Soc., Washington, DC) and Ernst, C. & Sumners, D. W. (1999) Math. Proc. Cambridge Philos. Soc. 126, 23-36]. PMID:15576510
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
The Application of Games Theory to Group Project Assessment.
ERIC Educational Resources Information Center
Pitt, M. J.
2000-01-01
Application of game theory to small-group project evaluation in higher education instruction finds that the best strategy for students wishing high grades may not be a strategy that promotes teamwork and cooperation. Suggests that putting students into groups may randomly disadvantage some students relative to others, producing serious unfairness…
Algebraic K-theory of discrete subgroups of Lie groups.
Farrell, F T; Jones, L E
1987-05-01
Let G be a Lie group (with finitely many connected components) and Gamma be a discrete, cocompact, torsion-free subgroup of G. We rationally calculate the algebraic K-theory of the integral group ring ZGamma in terms of the homology of Gamma with trivial rational coefficients. PMID:16593834
Algebraic K-theory of discrete subgroups of Lie groups
Farrell, F. T.; Jones, L. E.
1987-01-01
Let G be a Lie group (with finitely many connected components) and Γ be a discrete, cocompact, torsion-free subgroup of G. We rationally calculate the algebraic K-theory of the integral group ring ZΓ in terms of the homology of Γ with trivial rational coefficients. PMID:16593834
An Application of General System Theory (GST) to Group Therapy.
ERIC Educational Resources Information Center
Matthews, Charles O.
1992-01-01
Demonstrates the compatibility of General System Theory (GST) with the traditional counseling literature in explicating a therapy group's progression through Tuckman's (1965, 1977) developmental stages (forming, storming, norming, performing, and adjourning). Description uses both traditional group literature and GST concepts. (Author/NB)
Supporting Alternative Strategies for Learning Chemical Applications of Group Theory
ERIC Educational Resources Information Center
Southam, Daniel C.; Lewis, Jennifer E.
2013-01-01
A group theory course for chemists was taught entirely with process oriented guided inquiry learning (POGIL) to facilitate alternative strategies for learning. Students completed a test of one aspect of visuospatial aptitude to determine their individual approaches to solving spatial tasks, and were sorted into groups for analysis on the basis of…
Multiloop calculations in perturbative quantum field theory
NASA Astrophysics Data System (ADS)
Blokland, Ian Richard
This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for problems in a field of particle physics with a very rich history. The third calculation provides an improved prediction for the decay of a top quark. In order to obtain this result, a large class of multiloop integrals has been solved for the first time. Top quark decay is just one member of a family of interesting physical processes to which these new results apply. Since specialized calculational techniques are essential ingredients in all three calculations, they are motivated and explained carefully in this thesis. These techniques, once automated with symbolic computational software, have recently opened avenues of solution to a wide variety of important problems in particle physics.
Inhomogeneous field theory inside the arctic circle
NASA Astrophysics Data System (ADS)
Allegra, Nicolas; Dubail, Jérôme; Stéphan, Jean-Marie; Viti, Jacopo
2016-05-01
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point (Δ =0 ). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.
On conformal field theories with extremal values
NASA Astrophysics Data System (ADS)
Zhiboedov, Alexander
2014-04-01
Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy tensor. We analyze energy correlators in parity invariant four-dimensional CFTs. The goal is to use the positivity of energy correlators to further constrain unitary CFTs. It is known that the positivity of the simplest one-point energy correlator implies that where a and c are the Weyl anomaly coefficients. We use the positivity of higher point energy correlators to show that CFTs with extremal values of have trivial scattering observables. More precisely, for and all energy correlators are fixed to be the ones of the free boson and the free vector theory correspondingly. Similarly, we show that the positivity and finiteness of energy correlators together imply that the three-point function of the stress tensor in a CFT cannot be proportional to the one in the theory of free boson, free fermion or free vector field.
Group Dynamics in Janis's Theory of Groupthink: Backward and Forward.
McCauley
1998-02-01
Janis's groupthink theory is an appealing explanation of how group process can get in the way of optimal decision making. Unfortunately, Janis was selective and not always consistent in his application of research in group dynamics. This paper traces groupthink to its theoretical roots in order to suggest how a broader and more consistent use of research in group dynamics can advance understanding of decision-making problems. In particular, the paper explores and reinterprets the groupthink prediction that poor decision making is most likely when group cohesion is based on the personal attractiveness of group members. Copyright 1998 Academic Press. PMID:9705800
Bayesian parameter estimation for effective field theories
NASA Astrophysics Data System (ADS)
Wesolowski, S.; Klco, N.; Furnstahl, R. J.; Phillips, D. R.; Thapaliya, A.
2016-07-01
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
The effective field theory of dark energy
NASA Astrophysics Data System (ADS)
Gubitosi, Giulia; Piazza, Federico; Vernizzi, Filippo
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Time-dependent perturbation theory in quantum mechanics and the renormalization group
NASA Astrophysics Data System (ADS)
Bhattacharjee, J. K.; Ray, D. S.
2016-06-01
Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.
Anomaly cancelation in field theory and F-theory on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas
2016-05-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
QCD unitarity constraints on Reggeon Field Theory
NASA Astrophysics Data System (ADS)
Kovner, Alex; Levin, Eugene; Lublinsky, Michael
2016-08-01
We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
Thermalization of Strongly Coupled Field Theories
Balasubramanian, V.; Bernamonti, A.; Copland, N.; Craps, B.; Staessens, W.; Boer, J. de; Keski-Vakkuri, E.; Mueller, B.; Schaefer, A.; Shigemori, M.
2011-05-13
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.
Thermalization of strongly coupled field theories.
Balasubramanian, V; Bernamonti, A; de Boer, J; Copland, N; Craps, B; Keski-Vakkuri, E; Müller, B; Schäfer, A; Shigemori, M; Staessens, W
2011-05-13
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first. PMID:21668141
Compact boson stars in K field theories
NASA Astrophysics Data System (ADS)
Adam, C.; Grandi, N.; Klimas, P.; Sánchez-Guillén, J.; Wereszczyński, A.
2010-11-01
We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.
Scalar-field theory of dark matter
NASA Astrophysics Data System (ADS)
Huang, Kerson; Xiong, Chi; Zhao, Xiaofei
2014-05-01
We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein-Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Drift estimation from a simple field theory
Mendes, F. M.; Figueiredo, A.
2008-11-06
Given the outcome of a Wiener process, what can be said about the drift and diffusion coefficients? If the process is stationary, these coefficients are related to the mean and variance of the position displacements distribution. However, if either drift or diffusion are time-dependent, very little can be said unless some assumption about that dependency is made. In Bayesian statistics, this should be translated into some specific prior probability. We use Bayes rule to estimate these coefficients from a single trajectory. This defines a simple, and analytically tractable, field theory.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
XXIVth International Symposium on Lattice Field Theory
NASA Astrophysics Data System (ADS)
2006-12-01
Lattice 2006, the XXIV International Symposium on Lattice Field Theory, was held from July 23-28, 2006 at the Starr Pass Hotel near Tucson, Arizona, USA, hosted by the University of Arizona Physics Department. The scientific program contained 25 plenary session talks and 193 parallel session contributions (talks and posters). Topics in lattice QCD included: hadron spectroscopy; hadronic interactions and structure; algorithms, machines, and networks; chiral symmetry; QCD confinement and topology; quark masses, gauge couplings, and renormalization; electroweak decays and mixing; high temperature and density; and theoretical developments. Topics beyond QCD included large Nc, Higgs, SUSY, gravity, and strings.
Pauli-Villars regulatization of supergravity and field theory anomalies
Gaillard, M.K.
1995-06-01
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
The monster sporadic group and a theory underlying superstring models
Chapline, G.
1996-09-01
The pattern of duality symmetries acting on the states of compactified superstring models reinforces an earlier suggestion that the Monster sporadic group is a hidden symmetry for superstring models. This in turn points to a supersymmetric theory of self-dual and anti-self-dual K3 manifolds joined by Dirac strings and evolving in a 13 dimensional spacetime as the fundamental theory. In addition to the usual graviton and dilaton this theory contains matter-like degrees of freedom resembling the massless states of the heterotic string, thus providing a completely geometric interpretation for ordinary matter. 25 refs.
Towards a quantum field theory of primitive string fields
Ruehl, W.
2012-10-15
We denote generating functions of massless even higher-spin fields 'primitive string fields' (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher-spin fields have become known. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher-spin field theories in AdS{sub d+1} are determined by AdS/CFT correspondence from universality classes of critical systems in d-dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for 1 {<=} N {<=}{infinity} play for us the role of 'standard models', for varying N, they contain, e.g., the Ising model for N = 1 and the spherical model for N = {infinity}. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on AdS space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher-spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin s conformal higher-spin fields for all s {>=} 4, they are distinguished by their anomalous dimensions (in CFT{sub 3}) or by theirmass (in AdS{sub 4}). We sum over these multiplets and the spins to obtain 'string type fields', one for each such monomial.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
Conformal field theory of critical Casimir forces
NASA Astrophysics Data System (ADS)
Emig, Thorsten; Bimonte, Giuseppe; Kardar, Mehran
2015-03-01
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional conformal field theories (CFT) we derive exact results for the Casimir interaction for a deformed strip and for two compact objects of arbitrary shape in terms of the free energy of a standard region (circular ring or flat strip) whose dimension is determined by the mutual capacitance of two conductors with the objects' shape; and a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details. The effect of inhomogenous boundary conditions is also discussed.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Group theory and biomolecular conformation: I. Mathematical and computational models
Chirikjian, Gregory S
2010-01-01
Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes. PMID:20827378
Gauge gravitation theory: Gravity as a Higgs field
NASA Astrophysics Data System (ADS)
Sardanashvily, Gennadi
2016-05-01
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking, where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.
Ramond equations of motion in superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2015-11-01
We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
The spectral theory of a functional-difference operator in conformal field theory
NASA Astrophysics Data System (ADS)
Takhtajan, L. A.; Faddeev, L. D.
2015-04-01
We consider the functional-difference operator H=U+U-1+V, where U and V are the Weyl self-adjoint operators satisfying the relation UV=q2VU, q=eπ iτ, τ>0. The operator H has applications in the conformal field theory and representation theory of quantum groups. Using the modular quantum dilogarithm (a q-deformation of the Euler dilogarithm), we define the scattering solution and Jost solutions, derive an explicit formula for the resolvent of the self-adjoint operator H on the Hilbert space L2( R), and prove the eigenfunction expansion theorem. This theorem is a q-deformation of the well-known Kontorovich-Lebedev transform in the theory of special functions. We also present a formulation of the scattering theory for H.
Non-rigid molecular group theory and its applications
Balasubramanian, K.
1982-06-01
The use of generalized wreath product groups as representations of symmetry groups of nonrigid molecules is considered. Generating function techniques are outlined for nuclear spin statistics and character tables of the symmetry groups of nonrigid molecules. Several applications of nonrigid molecular group theory to NMR spectroscopy, rovibronic splitting and nuclear spin statistics of nonrigid molecules, molecular beam deflection and electric resonance experiments of weakly bound Van der Waal complexes, isomerization processes, configuration interaction calculations and the symmetry of crystals with structural distortions are described. 81 references.
Perfect magnetohydrodynamics as a field theory
Bekenstein, Jacob D.; Betschart, Gerold
2006-10-15
We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of ({Dirac_h}/2{pi}); this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
ERIC Educational Resources Information Center
Riva, Maria T.; Korinek, Lauri
2004-01-01
Training in group counseling typically includes an academic component, although little has been written about how to teach a group course except for what specific content should be included. This article suggests that while teaching group counseling courses, instructors can intentionally model effective group leader behaviors and use these…
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
On Finite Groups and Finite Fields.
ERIC Educational Resources Information Center
Reid, J. D.
1991-01-01
Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)
Power counting and Wilsonian renormalization in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
Male Reference Group Identity Dependence: A Theory of Male Identity.
ERIC Educational Resources Information Center
Wade, Jay C.
1998-01-01
Presents a theory of male identity developed to address the question of why men vary in their masculinity ideology and in their conformity to standards of masculinity. An overview of relevant masculinity research, theoretical foundations for the construct of reference group identity dependence, theoretical postulates, associated behavioral, and…
Effective field theory of quantum gravity coupled to scalar electrodynamics
NASA Astrophysics Data System (ADS)
Ibiapina Bevilaqua, L.; Lehum, A. C.; da Silva, A. J.
2016-05-01
In this work, we use the framework of effective field theory to couple Einstein’s gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where quantum mechanics and general relativity are perfectly compatible. We consider the effective field theory up to dimension six operators, corresponding to processes involving one-graviton exchange. Studying the renormalization group functions, we see that the beta function of the electric charge is positive and possesses no contribution coming from gravitational interaction. Our result indicates that gravitational corrections do not alter the running behavior of the gauge coupling constants, even if massive particles are present.
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
2006-03-01
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the "scale-space." We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
2014-03-01
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Statistical field theory of a nonadditive system
NASA Astrophysics Data System (ADS)
Olemskoi, A. I.; Yushchenko, O. V.; Badalyan, A. Yu.
2013-03-01
Based on quantum field methods, we develop a statistical theory of complex systems with nonadditive potentials. Using the Martin-Siggia-Rose method, we find the effective system Lagrangian, from which we obtain evolution equations for the most probable values of the order parameter and its fluctuation amplitudes. We show that these equations are unchanged under deformations of the statistical distribution while the probabilities of realizing different phase trajectories depend essentially on the nonadditivity parameter. We find the generating functional of a nonadditive system and establish its relation to correlation functions; we introduce a pair of additive generating functionals whose expansion terms determine the set of multipoint Green's functions and their self-energy parts. We find equations for the generating functional of a system having an internal symmetry and constraints. In the harmonic approximation framework, we determine the partition function and moments of the order parameter depending on the nonadditivity parameter. We develop a perturbation theory that allows calculating corrections of an arbitrary order to the indicated quantities.
Multidimensional wave field signal theory: Mathematical foundations
NASA Astrophysics Data System (ADS)
Baddour, Natalie
2011-06-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Irreversibility and higher-spin conformal field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2000-08-01
I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.
New Advocacy Groups Shaking up Education Field
ERIC Educational Resources Information Center
Sawchuk, Stephen
2012-01-01
A new generation of education advocacy groups has emerged to play a formidable political role in states and communities across the country. Those groups are shaping policy through aggressive lobbying and campaign activity--an evolution in advocacy that is primed to continue in the 2012 elections and beyond. Though the record of their electoral…
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Baker, W.M.
1980-01-01
We examine the scale-invariant Lagrangian densities in Riemannian and non-Riemannian spacetimes. We find that the most general scale-invariant Lagrangian density of a Riemann-Cartan spacetime can also be reduced in a manner similar to that demonstrated earlier by Lanczos for the Riemannian case. However, this type of reduction process is not possible in a non-metric spacetime. Duality transformations of the type defined in electromagnetic theory are discussed and classified in terms of those transformations having a direct relationship to an internal symmetry structure of a given gauge theory and those that do not. We show that to build a satisfactory generalized electromagnetic type theory with local duality invariance into a gauge theory, as at least a part of its internal symmetry structure, requires a group no smaller than SO/sub 3/ or (SU/sub 2/). By considering a special metric geometry with torsion (U/sub 4/) we can describe the duality vector field of a duality invariant Maxwell theory in terms of a special form of torsion. This result indicates that the special U/sub 4/ geometry could play a role in the already unified field theory of Rainich, Misner, and Wheeler (RMW). We show how one could express the RMW conditions, together with their immediate generalizations in terms of geometric objects of the special U/sub 4/ theory. Conformal and projective transformations on the U/sub 4/ connection are examined. It is shown that an appropriate combination of these transformations have the effect of producing a special type of projective transformation on a metric connection with torsion. In the context of a gauge theory based on a U/sub 4/ spacetime, this special type of projective invariance has been interpreted as the underlying invariance principle for baryon number conservation in the same way that gauge changes on the Maxwell vector potential relate to charge conservation.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
The Family FIRO Model: The Integration of Group Theory and Family Theory.
ERIC Educational Resources Information Center
Colangelo, Nicholas; Doherty, William J.
1988-01-01
Presents the Family Fundamental Interpersonal Relations Orientation (Family FIRO) Model, an integration of small-group theory and family therapy. The model is offered as a framework for organizing family issues. Discusses three fundamental issues of human relatedness and their applicability to group dynamics. (Author/NB)
Anomalies in non-polynomial closed string field theory
NASA Astrophysics Data System (ADS)
Kaku, Michio
1990-11-01
The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.
Trivial pursuits: studies in quantum field theory and squantum cosmology
Furlong, R.C.
1987-01-01
The author show that the nonrelativistic limit of the lambdaphi/sup 4/ theory is trivial in 1 + 3 dimensions; the renormalized coupling constant vanishes and the S matrix reduces to the unit matrix. Our result is consistent with, though not sufficient to establish, the triviality of the Lorentz-invariant theory. A necessary condition for the existence of a consistent non-trivial continuum quantum field theory in d = 4 is the existence of an ultraviolet-stable fixed point of the Gell-Mann-Low renormalization group. Since others have shown (non-perturbatively) that the existence of just such a fixed point is sufficient to guarantee the triviality of the continuum massless Wess-Zumino model, we conclude that this model cannot exist non-trivially in d = 4. The fact that most renormalization group blocking schemes include each site link in many block links can generate spurious interactions in the block system. A general method for avoiding this problem is formulated and applied to do a Monte Carlo renormalization group study of the SU(2)-Higgs model in four dimensions with a check 2 scale factor. Finally starting from the D'Eath equation, the Dirac square root of the Wheeler-De Witt equation, for N = 1 supergravity, we construct superminisuperspace models (and quasi-models) for supersymmetric quantum cosmology (squantum cosmology) compatibile with Friedmann-Robertson-Walker (FRW) cosmologies.
Fractional Loop Group and Twisted K-Theory
NASA Astrophysics Data System (ADS)
Hekmati, Pedram; Mickelsson, Jouko
2010-11-01
We study the structure of abelian extensions of the group L q G of q-differentiable loops (in the Sobolev sense), generalizing from the case of the central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of the supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on G is discussed.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Use of group theory for the analysis of vibrational spectra
NASA Astrophysics Data System (ADS)
Rykhlinskaya, K.; Fritzsche, S.
2004-09-01
To facilitate the use of group theory in the analysis of vibrational spectra, a set of Maple procedures is provided generating the normal coordinates and determining the spectral activities of polyatomic molecules. Our program, called BETHE, is based on the frequently applied point groups and provides an interactive access to the group data as needed in physical chemistry and elsewhere. Owing to the demand of the users the normal coordinates of the molecules are provided either in terms of Cartesian or internal coordinates. Program summaryTitle of program:BETHE Catalogue number: ADUH Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUH Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed: All computers with a license of the computer algebra package MAPLE Installations:University of Kassel (Germany) Operating systems under which the program has been tested: Linux 8.1+ and Windows 2000 Program language used:MAPLE 7 and 8 Memory required to execute with typical data: 10-30 MB No. of lines in distributed program including test data, etc.:11 859 No. of bytes in distributed program including test data, etc.:312 229 Distribution format:tar.gz Nature of the physical problem: Interaction of the infrared light with the molecule can lead to the excitation of the molecular vibrations [1]. Analysis of such vibrations is performed by the point group theory and helps to interpret the molecular spectra. Method of solution: Point group theory is applied to determine the normal coordinates of symmetric molecules and to carry out a spectroscopic analysis of their vibrational modes. The direct product of the irreducible representations is utilized to obtain the selection rules for infrared and Raman spectroscopy. Restrictions onto the complexity of the problem: The computation of the normal coordinates is supported for rather a large number of symmetries; in the present
Quarkonium hybrids with nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Berwein, Matthias; Brambilla, Nora; Tarrús Castellà, Jaume; Vairo, Antonio
2015-12-01
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass m of the heavy quark. At order 1 /m in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as Λ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for c c ¯, b c ¯, and b b ¯ hybrids. The Λ -doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.
Effective Field Theory for Rydberg Polaritons
NASA Astrophysics Data System (ADS)
Gullans, M. J.; Wang, Y.; Thompson, J. D.; Liang, Q.-Y.; Vuletic, V.; Lukin, M. D.; Gorshkov, A. V.
2016-05-01
Photons can be made to strongly interact by dressing them with atomic Rydberg states under conditions of electromagnetic induced transparency. Probing Rydberg polaritons in the few-body limit, recent experiments were able to observe non-perturbative two-body effects including: single photon switching and the formation of bound states. Although the two-body problem is amenable to exact solutions, such approaches quickly become intractable for more than two particles. To overcome this problem, we study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). For attractive interactions, we show how a suitably long medium can be used to prepare shallow N-body bound states in one dimension. We verify this prediction for two and three photons using full numerical simulations. We then consider conditions under which the effective interactions are repulsive and study two and three photon transmission. Finally, we show how to go beyond EFT by measuring the three-body contact force or, alternatively, scattering at high relative momenta.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (
Superconformal field theory and Jack superpolynomials
NASA Astrophysics Data System (ADS)
Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2012-09-01
We uncover a deep connection between the {N} = {1} superconformal field theory in 2 D and eigenfunctions of the supersymmetric Sutherland model known as Jack super-polynomials (sJacks). Specifically, the singular vector at level rs/2 of the Kac module labeled by the two integers r and s are given explicitly as a sum of sJacks whose indexing diagrams are contained in a rectangle with r columns and s rows. As a second compelling evidence for the distinguished status of the sJack-basis in SCFT, we find that the degenerate Whittaker vectors (Gaiotto states) can be expressed as a remarkably simple linear combination of sJacks. As a consequence, we are able to reformulate the supersymmetric version of the (degenerate) AGT conjecture in terms of the combinatorics of sJacks. The closed-form formulas for the singular vectors and the degenerate Whittaker vectors, although only conjectured in general, have been heavily tested (in some cases, up to level 33/2). Both the Neveu-Schwarz and Ramond sectors are treated.
Logarithmic conformal field theory: a lattice approach
NASA Astrophysics Data System (ADS)
Gainutdinov, A. M.; Jacobsen, J. L.; Read, N.; Saleur, H.; Vasseur, R.
2013-12-01
Logarithmic conformal field theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self-avoiding walks, etc), or of critical points in several classes of disordered systems (transition between plateaux in the integer and spin quantum Hall effects). Much progress in their understanding has been obtained by studying algebraic features of their lattice regularizations. For reasons which are not entirely understood, the non-semi-simple associative algebras underlying these lattice models—such as the Temperley-Lieb algebra or the blob algebra—indeed exhibit, in finite size, properties that are in full correspondence with those of their continuum limits. This applies not only to the structure of indecomposable modules, but also to fusion rules, and provides an ‘experimental’ way of measuring couplings, such as the ‘number b’ quantifying the logarithmic coupling of the stress-energy tensor with its partner. Most results obtained so far have concerned boundary LCFTs and the associated indecomposability in the chiral sector. While the bulk case is considerably more involved (mixing in general left and right moving sectors), progress has also recently been made in this direction, uncovering fascinating structures. This study provides a short general review of our work in this area.
Group Decisions in Biodiversity Conservation: Implications from Game Theory
Frank, David M.; Sarkar, Sahotra
2010-01-01
Background Decision analysis and game theory [1], [2] have proved useful tools in various biodiversity conservation planning and modeling contexts [3]–[5]. This paper shows how game theory may be used to inform group decisions in biodiversity conservation scenarios by modeling conflicts between stakeholders to identify Pareto–inefficient Nash equilibria. These are cases in which each agent pursuing individual self–interest leads to a worse outcome for all, relative to other feasible outcomes. Three case studies from biodiversity conservation contexts showing this feature are modeled to demonstrate how game–theoretical representation can inform group decision-making. Methodology and Principal Findings The mathematical theory of games is used to model three biodiversity conservation scenarios with Pareto–inefficient Nash equilibria: (i) a two–agent case involving wild dogs in South Africa; (ii) a three–agent raptor and grouse conservation scenario from the United Kingdom; and (iii) an n–agent fish and coral conservation scenario from the Philippines. In each case there is reason to believe that traditional mechanism–design solutions that appeal to material incentives may be inadequate, and the game–theoretical analysis recommends a resumption of further deliberation between agents and the initiation of trust—and confidence—building measures. Conclusions and Significance Game theory can and should be used as a normative tool in biodiversity conservation contexts: identifying scenarios with Pareto–inefficient Nash equilibria enables constructive action in order to achieve (closer to) optimal conservation outcomes, whether by policy solutions based on mechanism design or otherwise. However, there is mounting evidence [6] that formal mechanism–design solutions may backfire in certain cases. Such scenarios demand a return to group deliberation and the creation of reciprocal relationships of trust. PMID:20523732
Next-to-simplest quantum field theories
NASA Astrophysics Data System (ADS)
Lal, Shailesh; Raju, Suvrat
2010-05-01
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
Next-to-simplest quantum field theories
Lal, Shailesh; Raju, Suvrat
2010-05-15
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
NASA Astrophysics Data System (ADS)
Zatloukal, Václav
2016-04-01
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.
Some aspects of the theory of quantum groups
NASA Astrophysics Data System (ADS)
Demidov, E. E.
1993-12-01
CONTENTSIntroductionChapter I. Basic constructions § 1. Definition of a Hopf algebra § 2. Two constructions of quantum semigroups § 3. Universal coacting and R-matrix algebras § 4. The quantum determinant and antipode § 5. The dimension of quantum semigroupsChapter II. Representation theory § 6. Basic concepts of representation theory § 7. The quantum flag space of \\operatorname{GL}_{P, \\mathcal Q, c}(n) § 8. The Schur algebra and complete reducibility § 9. Representations of \\operatorname{SL}_J(2) §10. The Frobenius morphismChapter III. Non-commutative differential calculus §11. The non-commutative de Rham complex of an n-dimensional vector space §12. Quantum Weyl algebras §13. The de Rham complex of a quantum groupReferences
Mean field theory for long chain molecules
NASA Astrophysics Data System (ADS)
Pereira, Gerald G.
1996-06-01
We provide a mathematical formalism for a self-consistent mean field treatment of long chain molecules. The formalism is applied to the case of a neutral polymer under the excluded volume interaction. Upon scaling the problem in the N→∞ limit we find the natural scaling length RN, of the polymer, which is made up of (N+1) monomers or beads, is RN˜N3/5, the well known Flory result. The asymptotics of the problem is dominated by the neighborhood of the turning point, so that a uniformly valid Green's function solution of the differential equations is necessary. In the neighborhood of a point y* the scaled polymer density fN(x), is found to decay sharply. If we let x denote the scaled distance from one end of the chain to a point in space we obtain, for y*-x≳O(N-2/15), a closed form expression for the polymer density viz., fN(x)˜{1/2x2[fN(x)-fN(y*)]1/2} while for x-y*≳O(N-2/15) the density is shown to be, to leading order, zero. Although our results imply the rate of decay of the density at y* is O(N1/5) we are unable to verify this explicitly by calculating fN'(y*). We believe this is due to the inability of the WKB theory to correctly approximate solutions in regions of rapid variation. We suggest remedies for this, so that a complete self-consistent solution may be obtained.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
Review and application of group theory to molecular systems biology.
Rietman, Edward A; Karp, Robert L; Tuszynski, Jack A
2011-01-01
In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer. PMID:21696623
Review and application of group theory to molecular systems biology
2011-01-01
In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer. PMID:21696623
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf; Ludwig, Thomas; Verch, Rainer
2013-02-15
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Quiver theories for moduli spaces of classical group nilpotent orbits
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Kalveks, Rudolph
2016-06-01
We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3 d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKähler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for their decompositions into characters of irreducible representations and/or Hall Littlewood polynomials.
Effective field theory of broken spatial diffeomorphisms
NASA Astrophysics Data System (ADS)
Lin, Chunshan; Labun, Lance Z.
2016-03-01
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Reggeon Field Theory and the phases of QCD
White, A.R.
1987-07-21
We propose a Reggeon Field Theory phase diagram involving Sub-critical and Super-critical Pomeron behavior and the Expanding Disc. We describe the derivation of Reggeon Field Theory from QCD using infra-red analysis of the reggeon diagrams of the spontaneously broken theory. Matching the Reggeon Field Theory phase-diagram to that of lattice QCD with many fermions has significant implications for the chiral properties of continuum QCD when the number of flavors is less than the maximum allowed by asymptotic freedom. 19 refs., 7 figs.
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Exploring Group Cohesion in a Higher Education Field Experience
ERIC Educational Resources Information Center
Malcarne, Brian Keith
2012-01-01
The purpose of this study was to gain understanding into the experience of group cohesion for university students participating in an academic field experience. A mixed methods approach was used following a two-phase, sequential research design to help provide a more complete explanation of how group cohesion was impacted by the field experience.…
NS-NS sector of closed superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2014-08-01
We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.
Effective field theory: A modern approach to anomalous couplings
Degrande, Céline; Centre for Particle Physics and Phenomenology , Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve ; Greiner, Nicolas; Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München ; Kilian, Wolfgang; University of Siegen, Fachbereich Physik, D-57068 Siegen ; Mattelaer, Olivier; Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott; Zhang, Cen; Centre for Particle Physics and Phenomenology , Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve
2013-08-15
We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics.
Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
Bücher, David; Runkel, Ingo
2014-11-15
In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.
Soft theorems from effective field theory
NASA Astrophysics Data System (ADS)
Larkoski, Andrew J.; Neill, Duff; Stewart, Iain W.
2015-06-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
Nonlocal Stochastic Model for the Free Scalar Field Theory
NASA Astrophysics Data System (ADS)
Namsrai, Kh.
1981-05-01
The free scalar field is investigated within the framework of the Davidson stochastic model and of the hypothesis on space-time stochasticity. It is shown that the resulting Markov field obtained by averaging in this space-time is equivalent to a nonlocal Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter ν. Our result generalizes Guerra and Ruggiero's procedure of stochastic quantization of scalar fields. On the basis of the assumption about unobservability of ν in quantum field theory, the Efimov nonlocal theory is obtained from Euclidean Markov field with form factors of the class of entire analytical functions.
Universal behavior after a quantum quench in interacting field theories
NASA Astrophysics Data System (ADS)
Mitra, Aditi
The dynamics of an isolated quantum system represented by a field theory with O(N) symmetry, and in d>2 spatial dimensions, is investigated after a quantum quench from a disordered initial state to the critical point. A perturbative renormalization-group approach involving an expansion around d=4 is employed to study the time-evolution, and is supplemented by an exact solution of the Hartree-Fock equations in the large-N limit. The results show that the dynamics is characterized by a prethermal regime controlled by elastic dephasing where excitations propagate ballistically, and a light cone emerges in correlation functions in real space. The memory of the initial state, together with the absence of time-scales at the critical point, gives rise to universal power-law aging which is characterized by a new non-equilibrium short-time exponent. The dynamics of the entanglement following a quench is also explored, and reveals that while the time evolution of the entanglement entropy itself is not much different between a free bosonic theory and an interacting bosonic theory, the low-energy entanglement spectrum on the other hand shows clear signature of the non-equilibrium short-time exponent related to aging. This work was done in collaboration with Y. Lemonik (NYU), M. Tavora (NYU), A. Chiocchetta (SISSA), A. Maraga (SISSA), and A. Gambassi (SISSA). Supported by NSF-DMR 1303177.
Comparisons and connections between mean field dynamo theory and accretion disc theory
NASA Astrophysics Data System (ADS)
Blackman, E. G.
2010-01-01
The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.
Thermofield Dynamics for Twisted POINCARÉ-INVARIANT Field Theories:. Wick Theorem and S-Matrix
NASA Astrophysics Data System (ADS)
Leineker, Marcelo; Queiroz, Amilcar R.; Santana, Ademir E.; de Assis Siqueira, Chrystian
Poincaré invariant quantum field theories can be formulated on noncommutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincaré group is suitably twisted. In the present work we present a twisted Poincaré invariant quantum field theory at finite temperature. For that we use the formalism of thermofield dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a nontrivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.
Effective field theory for Higgs boson plus jet production
NASA Astrophysics Data System (ADS)
Dawson, S.; Lewis, I. M.; Zeng, Mao
2014-11-01
We use an effective field theory which includes all possible gluon-Higgs dimension-5 and dimension-7 operators to study Higgs boson plus jet production in next-to-leading order QCD. The effective field theory sheds light on the effect of a finite top quark mass as well as any beyond-the-Standard-Model modifications of Higgs-gluon effective couplings. In the gluon channel, the accuracy of the heavy-top approximation for differential distributions arises from the noninterference between the helicity amplitudes of the G3h and G2h operators in the mh
Field Theory Model of the Flyby Anomaly
Lewis, R. A
2009-03-16
Precision tracking of spacecraft on interplanetary missions has turned up several anomalous deviations from predictions of general relativity. The Flyby Anomaly, wherein spacecraft gain or lose energy in an earth-centric frame after an encounter with earth, is clearly associated with the rotation of the earth. The possibility that the missing ingredient is a new type of potential field surrounding the earth is assessed in this write-up. A scalar field with the kinetic energy distribution of the earth as a source is evaluated numerically, with an amplitude parameter adjusted to match the data of Anderson et al.(2008). The new field can be interpreted as a coupling between kinetic energies of objects, a field analogous to fluid mechanics, or a field coupled to acceleration. The potential field violates various aspects of standard physics, such as energy non-conservation.
Unified Field Theory and Force Formulas of Interactions
NASA Astrophysics Data System (ADS)
Ma, Tian; Wang, Shouhong
2013-04-01
The main objective of this talk is to drive a unified field model coupling four interactions, based on the principle of interaction dynamics (PID) and the principle of representation invariance (PID). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint. PRI requires that physical laws be independent of representations of the gauge groups. One important outcome of this unified field model is a natural duality between the interacting fields (g, A, W^a, S^k), corresponding to graviton, photon, intermediate vector bosons W^± and Z and gluons, and the adjoint bosonic fields (φ,, ^aw, ^ks). This duality predicts two Higgs particles of similar mass with one due to weak interaction and the other due to strong interaction. PID and PRI can be applied directly to individual interactions, leading to 1) modified Einstein equations, giving rise to a unified theory for dark matter and dark energy, 2) three levels of strong interaction potentials for quark, nucleon/hadron, and atom respectively, and 3) a weak interaction potential. These potential/force formulas offer a clear mechanism for both quark confinement and asymptotic freedom.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Open superstring field theory on the restricted Hilbert space
NASA Astrophysics Data System (ADS)
Konopka, Sebastian; Sachs, Ivo
2016-04-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
NASA Astrophysics Data System (ADS)
Keltikangas, K.; Wallén, H.
2010-10-01
This paper investigates electrical engineers' perceptions on their education in Finland, with particular emphasis on the basic electromagnetic field theory courses and their applicability in working life, using two online surveys (n=99 and n=120). The answers show a reasonably good satisfaction with the electrical engineering studies in general, but limited practical usefulness of the field theory courses in working life. However, both respondent groups mentioned that electromagnetic field theory should belong to the basic electrical engineering curriculum, which suggests a need to strengthen the connections between the different topics in the curriculum to enable a better holistic understanding of electrical engineering.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Lorentz symmetric quantum field theory for symplectic fermions
Robinson, Dean J.; Kapit, Eliot; LeClair, Andre
2009-11-15
A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a Klein-Gordon Lagrangian. This theory is shown to have all the required properties of a consistent free quantum field theory, namely, causality, unitarity, adherence to the spin-statistics theorem, CPT symmetry, and the Hermiticity and positive definiteness of the Hamiltonian. The global symmetry of the free theory is Sp(4){approx_equal}SO(5). Possible interacting theories of both the pseudo-Hermitian and Hermitian variety are then examined briefly.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
Lorentz symmetry breaking as a quantum field theory regulator
NASA Astrophysics Data System (ADS)
Visser, Matt
2009-07-01
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just “how much” Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Hořava’s recent article [Phys. Rev. DPRVDAQ1550-7998 79, 084008 (2009)10.1103/PhysRevD.79.084008] on 3+1 dimensional quantum gravity.
Applying Power Theories to Field Settings.
ERIC Educational Resources Information Center
Liss, Lora
To test theories presented in the sociology course "Social Policies and Community Power Structure," a team of undergraduate students and their instructor attended a national professional conference. The following are examples of those concepts the students observed in operation at the conference: Social structure affects social policies; the…
A class of effective field theory models of cosmic acceleration
NASA Astrophysics Data System (ADS)
Bloomfield, Jolyon K.; Flanagan, Éanna É.
2012-10-01
We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.
Renormalization group theory for Kondo breakdown in Kondo lattice systems
NASA Astrophysics Data System (ADS)
Ballmann, K.; Nejati, A.; Kroha, J.
2015-03-01
We present a renormalization group (RG) theory for the breakdown of Kondo screening in the Kondo lattice model (KLM) without pre-assumptions about the competition between Kondo effect and magnetic ordering or Fermi surface criticality. We show that the vertex between a single, local Kondo spin and the extended conduction electrons obtains RKKY- induced, non-local contributions in the in-and out-going coordinates of scattering electrons due to scattering at surrounding Kondo sites, but it remains local in the Kondo spin position. This enables the existence of a local Kondo screening scale TK(y) in the KLM, controlled by the effective RKKY coupling parameter y. TK(y) is determined by the RG flow of the local spin exchange coupling in the presence of the self-consistent spin response on surrounding Kondo sites. We show that TK(y) exhibits universal behavior and is suppressed by the antiferromagnetic RKKY coupling. Beyond a maximal RKKY parameter value ymax Kondo screening ceases to exist even without magnetic ordering. The theory opens up the possibility of describing quantum critical scenarios involving spin wave instabilities or local Kondo breakdown on the same footing.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Fermionic field theory for trees and forests.
Caracciolo, Sergio; Jacobsen, Jesper Lykke; Saleur, Hubert; Sokal, Alan D; Sportiello, Andrea
2004-08-20
We prove a generalization of Kirchhoff's matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a q-->0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that this latter model can be mapped, to all orders in perturbation theory, onto the N-vector model at N=-1 or, equivalently, onto the sigma model taking values in the unit supersphere in R(1|2). It follows that, in two dimensions, this fermionic model is perturbatively asymptotically free. PMID:15447166
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Killing vector fields and harmonic superfield theories
NASA Astrophysics Data System (ADS)
Groeger, Josua
2014-09-01
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
Geometrical Effective Action: Gauge Field Theory Without Ghosts.
NASA Astrophysics Data System (ADS)
Paris, Carmen Molina
Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph. Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions^1, obtaining thereby a mode sum over tree functions. It is easy to show that tree functions are gauge invariant provided the external lines bear only physical mode functions. Feynman therefore proposed to restrict the mode sums to physical modes, a procedure that not only secures gauge invariance but unitarity as well. But there is a difficulty: Because the physical mode functions are defined in a special frame, the procedure is not manifestly Lorentz invariant ^2. Feynman was able to show that deletion of the nonphysical modes is equivalent to subtracting, from the contribution of every closed loop, that of another (Lorentz invariant) loop propagating a particle having spin 1 (or one less than that of the gauge field). This is the ghost. Because its contribution is subtracted, it is a fermion. Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show
NASA Astrophysics Data System (ADS)
Méliot, Pierre-Loïc
2010-12-01
In this thesis, we investigate the asymptotics of random partitions chosen according to probability measures coming from the representation theory of the symmetric groups S_n and of the finite Chevalley groups GL(n,F_q) and Sp(2n,F_q). More precisely, we prove laws of large numbers and central limit theorems for the q-Plancherel measures of type A and B, the Schur-Weyl measures and the Gelfand measures. Using the RSK algorithm, it also gives results on longest increasing subsequences in random words. We develop a technique of moments (and cumulants) for random partitions, thereby using the polynomial functions on Young diagrams in the sense of Kerov and Olshanski. The algebra of polynomial functions, or observables of Young diagrams is isomorphic to the algebra of partial permutations; in the last part of the thesis, we try to generalize this beautiful construction.
Statistical field theories deformed within different calculi
NASA Astrophysics Data System (ADS)
Olemskoi, A. I.; Borysov, S. S.; Shuda, I. A.
2010-09-01
Within the framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis and generalized by Naudts, we develop field-theoretical schemes of statistically distributed fields. We construct a set of generating functionals and find their connection with corresponding correlators for basic-deformed, finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of additive functionals, which expansions into deformed series yield both Green functions and their irreducible proper vertices. We find as well formal equations, governing by the generating functionals of systems which possess a symmetry with respect to a field variation and are subjected to an arbitrary constrain. Finally, we generalize field-theoretical schemes inherent in concrete calculi in the Naudts manner. From the physical point of view, we study dependences of both one-site partition function and variance of free fields on deformations. We show that within the basic-deformed statistics dependence of the specific partition function on deformation has in logarithmic axes symmetrical form with respect to maximum related to deformation absence; in case of the finite-difference statistics, the partition function takes non-deformed value; for the Kaniadakis statistics, curves of related dependences have convex symmetrical form at small curvatures of the effective action and concave form at large ones. We demonstrate that only moment of the second order of free fields takes non-zero values to be proportional to inverse curvature of effective action. In dependence of the deformation parameter, the free field variance has linearly arising form for the basic-deformed distribution and increases non-linearly rapidly in case of the finite-difference statistics; for more complicated case of the Kaniadakis distribution, related dependence has double-well form.
Using Self Consistent Field Theory on Polymeric Mixtures
NASA Astrophysics Data System (ADS)
von Konigslow, Kier; Park, Chul; Thompson, Russell
The ability to predict the solubility of a particular solvent in a polymer fluid is essential to the production of polymer foams. For the past 40 years, the primary model employed to this end has been an expansion of Flory-Huggins lattice fluid theory developed by Sanchez and Lacombe (S-L theory). S-L theory, while useful in the uniform limit, is limited to homogeneous systems. Self-Consistent Field Theory (SCFT), which has long been in use in polymer physics, is a mean-field theory capable of modeling the equilibrium behaviour of both homogeneous and inhomogeneous systems. We are investigating whether SCFT, applied to polymer-solvent mixtures, is in agreement with SL-theory in the homogeneous limit. Should this prove successful, we hope to use SCFT to model more general mixtures, including inhomogeneous nanocellular polymer foam systems.
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
Lattice Study of Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
Winterowd, Christopher; Detar, Carleton; Zafeiropoulos, Savvas
2016-03-01
The discovery of graphene ranks as one of the most important developments in condensed matter physics in recent years. As a strongly interacting system whose low-energy excitations are described by the Dirac equation, graphene has many similarities with other strongly interacting field theories, particularly quantum chromodynamics (QCD). Graphene, along with other relativistic field theories, have been predicted to exhibit spontaneous symmetry breaking (SSB) when an external magnetic field is present. Using nonperturbative methods developed to study QCD, we study the low-energy effective field theory (EFT) of graphene subject to an external magnetic field. We find strong evidence supporting the existence of SSB at zero-temperature and characterize the dependence of the chiral condensate on the external magnetic field. We also present results for the mass of the Nambu-Goldstone boson and the dynamically generated quasiparticle mass that result from the SSB.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Fractal tracer distributions in turbulent field theories
NASA Astrophysics Data System (ADS)
Hansen, Jonas Lundbek; Bohr, Tomas
1998-07-01
We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and thereby find a regime in which the particle distribution is a strange attractor. We compare the Lyapunov dimension to the information dimension of actual particle distributions and show that there is good agreement with the Kaplan-Yorke conjecture. Similar phenomena have been observed experimentally.
Holographic thermal field theory on curved spacetimes
NASA Astrophysics Data System (ADS)
Marolf, Donald; Rangamani, Mukund; Wiseman, Toby
2014-03-01
The AdS/CFT correspondence relates certain strongly-coupled CFTs with large effective central charge ceff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly-coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma-balls, which become stable at large ceff. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame.
On-Shell Recursion Relations for Effective Field Theories.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2016-01-29
We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible. PMID:26871321
The mass-zero spin-two field and gravitational theory.
NASA Technical Reports Server (NTRS)
Coulter, C. A.
1972-01-01
Demonstration that the conventional theory of the mass-zero spin-two field with sources introduces extraneous nonspin-two field components in source regions and fails to be covariant under the full or restricted conformal group. A modified theory is given, expressed in terms of the physical components of mass-zero spin-two field rather than in terms of 'potentials,' which has no extraneous components inside or outside sources, and which is covariant under the full conformal group. For a proper choice of source term, this modified theory has the correct Newtonian limit and automatically implies that a symmetric second-rank source tensor has zero divergence. It is shown that possibly a generally covariant form of the spin-two theory derived here can be constructed to agree with general relativity in all currently accessible experimental situations.
Prolonged Field Care Working Group Fluid Therapy Recommendations.
Baker, Benjamin L; Powell, Doug; Riesberg, Jamie; Keenan, Sean
2016-01-01
The Prolonged Field Care Working Group concurs that fresh whole blood (FWB) is the fluid of choice for patients in hemorrhagic shock, and the capability to transfuse FWB should be a basic skill set for Special Operations Forces (SOF) Medics. Prolonged field care (PFC) must also address resuscitative and maintenance fluid requirements in nonhemorrhagic conditions. PMID:27045508
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Advances in reversed field pinch theory and computation
Schnack, D.D.; Ho, Y.L.; Carreras, B.A.; Sidikman, K.; Craddock, G.G.; Mattor, N.; Nebel, R.A.; Prager, S.C.; Terry, P.W.; Zita, E.J.
1992-12-31
Advances in theory and computations related to the reversed field pinch (RFP) are presented. These are: (1) the effect of the dynamo on thermal transport; (2) a theory of ion heating due to dynamo fluctuations; (3) studies of active and passive feedback schemes for controlling dynamo fluctuations; and (4) an analytic model for coupled g-mode and rippling turbulence in the RFP edge.
Theory of a quantum noncanonical field in curved spacetimes
Indurain, Javier; Liberati, Stefano
2009-08-15
Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from special relativity in the form of a deformed Poincare algebra. These proposals go generically under the name of doubly or deformed special relativity (DSR). In this article we further explore a recently proposed class of quantum field theories, involving noncanonically commuting complex scalar fields, which have been shown to entail a DSR-like symmetry. An open issue for such theories is whether the DSR-like symmetry has to be taken as a physically relevant symmetry, or if in fact the 'true' symmetries of the theory are just rotations and translations while boost invariance has to be considered broken. Here we analyze this issue by extending the known results to curved spacetime under both of the previous assumptions. We show that if the symmetry of the free theory is taken to be a DSR-like realization of the Poincare symmetry, then it is not possible to render such a symmetry a gauge symmetry of the curved physical spacetime. However, it is possible to introduce an auxiliary spacetime which allows one to describe the theory as a standard quantum field theory in curved spacetime. Alternatively, taking the point of view that the noncanonical commutation of the fields actually implies a breakdown of boost invariance, the physical spacetime manifold has to be foliated in surfaces of simultaneity, and the field theory can be coupled to gravity by making use of the Arnowitt-Deser-Misner prescription.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Topological field theory amplitudes for A N-1 fibration
NASA Astrophysics Data System (ADS)
Iqbal, Amer; Khan, Ahsan Z.; Qureshi, Babar A.; Shabbir, Khurram; Shehper, Muhammad A.
2015-12-01
We study the partition function N=1 5D U( N) gauge theory with g adjoint hypermultiplets and show that for massless adjoint hypermultiplets it is equal to the partition function of a two dimensional topological field on a genus g Riemann surface. We describe the topological field theory by its amplitudes associated with cap, propagator and pair of pants. These basic amplitudes are open topological string amplitudes associated with certain Calabi-Yau threefolds in the presence of Lagrangian branes.
Central charge bounds in 4D conformal field theory
Rattazzi, Riccardo; Vichi, Alessandro; Rychkov, Slava
2011-02-15
We derive model-independent lower bounds on the stress tensor central charge C{sub T} in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C{sub T} is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.
Non-perturbative methods in relativistic field theory
Franz Gross
2013-03-01
This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.
Effective field theory from modified gravity with massive modes
NASA Astrophysics Data System (ADS)
Capozziello, Salvatore; de Laurentis, Mariafelicia; Paolella, Mariacristina; Ricciardi, Giulia
2015-10-01
Massive gravitational modes in effective field theories can be recovered by extending General Relativity and taking into account generic functions of the curvature invariants, not necessarily linear in the Ricci scalar R. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed.
Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
NASA Astrophysics Data System (ADS)
Szabo, Richard J.; Valentino, Alessandro
2010-03-01
We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.
On the entanglement between interacting scalar field theories
NASA Astrophysics Data System (ADS)
Mozaffar, M. Reza Mohammadi; Mollabashi, Ali
2016-03-01
We study "field space entanglement" in certain quantum field theories consisting of N number of free scalar fields interacting with each other via kinetic mixing terms. We present exact analytic expressions for entanglement and Renyi entropies between arbitrary numbers of scalar fields by which we could explore certain entanglement inequalities. Other entanglement measures such as mutual information and entanglement negativity have also been studied. We also give some comments about possible holographic realizations of such models.
Quantum theory for plasmon-assisted local field enhancement
NASA Astrophysics Data System (ADS)
Grigorenko, Ilya
2016-01-01
We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.
Quantum theory for plasmon-assisted local field enhancement
NASA Astrophysics Data System (ADS)
Grigorenko, Ilya
We applied quantum theory for nonlocal response and plasmon-assisted field enhancement near a small metallic nanoscale antenna in the limit of weak incoming fields. A simple asymmetric bio-inspired design of the nanoantenna for polarization-resolved measurement is proposed. The spatial field intensity distribution was calculated for different field frequencies and polarizations. We have shown that the proposed design the antenna allows us to resolve the polarization of incoming photons.
Near-field environment/processes working group summary
Murphy, W.M.
1995-09-01
This article is a summary of the proceedings of a group discussion which took place at the Workshop on the Role of Natural Analogs in Geologic Disposal of High-Level Nuclear Waste in San Antonio, Texas on July 22-25, 1991. The working group concentrated on the subject of the near-field environment to geologic repositories for high-level nuclear waste. The near-field environment may be affected by thermal perturbations from the waste, and by disturbances caused by the introduction of exotic materials during construction of the repository. This group also discussed the application of modelling of performance-related processes.
Black holes from generalized gauge field theories
NASA Astrophysics Data System (ADS)
Diaz-Alonso, J.; Rubiera-Garcia, D.
2011-02-01
We summarize the main results of a broad analysis on electrostatic, spherically symmetric (ESS) solutions of a class of non-linear electrodynamics models minimally coupled to gravitation. Such models are defined as arbitrary functions of the two quadratic field invariants, constrained by several physical admissibility requirements, and split into different families according to the behaviour of these lagrangian density functions in vacuum and on the boundary of their domains of definition. Depending on these behaviours the flat-space energy of the ESS field can be finite or divergent. For each model we qualitatively study the structure of its associated gravitational configurations, which can be asymptotically Schwarzschild-like or with an anomalous non Schwarzschild-like behaviour at r → ∞ (but being asymptotically flat and well behaved anyhow). The extension of these results to the non-abelian case is also briefly considered.
Effective hydrodynamic field theory and condensation picture of topological insulators
NASA Astrophysics Data System (ADS)
Chan, AtMa P. O.; Kvorning, Thomas; Ryu, Shinsei; Fradkin, Eduardo
2016-04-01
While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac boundary spectrum, it remains elusive to develop a hydrodynamic or collective description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a U (1 ) gauge field that arises by gauging the continuous symmetry of the target system [the U (1 ) particle number conservation]. Integrating over the U (1 ) gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the U (1 ) gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description of the surface of topological insulators and the implication of its duality are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Koenig, Robert
2015-03-01
We give restrictions on the locality-preserving unitary automorphisms U, which are protected gates, for topologically ordered systems. For arbitrary anyon models, we show that such unitaries only generate a finite group, and hence do not provide universality. For abelian anyon models, we find that the logical action of U is contained in a proper subgroup of the generalized Clifford group. In the case D(?2), which describes Kitaev's toric code, this represents a tightening of statement previously obtained within the stabilizer framework (PRL 110:170503). For non-abelian models, we find that such automorphisms are very limited: for example, there is no non-trivial gate for Fibonacci anyons. For Ising anyons, protected gates are elements of the Pauli group. These results are derived by relating such automorphisms to symmetries of the underlying anyon model: protected gates realize automorphisms of the Verlinde algebra. We additionally use the compatibility with basis changes to characterize the logical action. This is joint work with M. Beverland, F. Pastawski, J. Preskill and S. Sijher.
Quantum field theory of interacting plasmon-photon-phonon system
NASA Astrophysics Data System (ADS)
Hieu Nguyen, Van; Nguyen, Bich Ha
2015-09-01
This work is devoted to the construction of the quantum field theory of the interacting system of plasmons, photons and phonons on the basis of general fundamental principles of electrodynamics and quantum field theory of many-body systems. Since a plasmon is a quasiparticle appearing as a resonance in the collective oscillation of the interacting electron gas in solids, the starting point is the total action functional of the interacting system comprising electron gas, electromagnetic field and phonon fields. By means of the powerful functional integral technique, this original total action is transformed into that of the system of the quantum fields describing plasmons, transverse photons, acoustic as well as optic longitudinal and transverse phonons. The collective oscillations of the electron gas is characterized by a real scalar field φ(x) called the collective oscillation field. This field is split into the static background field φ0(x) and the fluctuation field ζ(x). The longitudinal phonon fields {{{Q}}al}(x), {{{Q}}ol}(x) are also split into the background fields {Q}0al(x), {Q}0ol(x) and dynamical fields {{{q}}al}(x), {{{q}}ol}(x) while the transverse phonon fields {{{Q}}at}(x), {{{Q}}ot}(x) themselves are dynamical fields {{{q}}at}(x), {{{q}}ot}(x) without background fields. After the canonical quantization procedure, the background fields φ0(x), {Q}0al(x), {Q}0ol(x) remain the classical fields, while the fluctuation fields ζ(x) and dynamical phonon fields {{{q}}al}(x), {{{q}}at}(x), {{{q}}ol}(x), {{{q}}ot}(x) become quantum fields. In quantum theory, a plasmon is the quantum of Hermitian scalar field σ(x) called the plasmon field, longitudinal phonons as complex spinless quasiparticles are the quanta of the effective longitudinal phonon Hermitian scalar fields {{θ }a}(x), {{θ }0}(x), while transverse phonons are the quanta of the original Hermitian transverse phonon vector fields {{{q}}at}(x), {{{q}}ot}(x). By means of the functional integral
Improved renormalization group theory for critical asymmetry of fluids
NASA Astrophysics Data System (ADS)
Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun
2013-09-01
We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Fundamental string solutions in open string field theories
Michishita, Yoji
2006-02-15
In Witten's open cubic bosonic string field theory and Berkovits' superstring field theory we investigate solutions of the equations of motion with appropriate source terms, which correspond to Callan-Maldacena solution in Born-Infeld theory representing fundamental strings ending on the D-branes. The solutions are given in order by order manner, and we show some full order properties in the sense of {alpha}{sup '} expansion. In superstring case we show that the solution is 1/2 BPS in full order.
Equivariant algebraic vector bundles over representations of reductive groups: theory.
Masuda, M; Petrie, T
1991-01-01
Let G be a reductive algebraic group and let B be an affine variety with an algebraic action of G. Everything is defined over the field C of complex numbers. Consider the trivial G-vector bundle B x S = S over B where S is a G-module. From the endomorphism ring R of the G-vector bundle S a construction of G-vector bundles over B is given. The bundles constructed this way have the property that when added to S they are isomorphic to F + S for a fixed G-module F. For such a bundle E an invariant rho(E) is defined that lies in a quotient of R. This invariant allows us to distinguish nonisomorphic G-vector bundles. This is applied to the case where B is a G-module and, in that case, an invariant of the underlying equivariant variety is given too. These constructions and invariants are used to produce families of inequivalent G-vector bundles over G-modules and families of inequivalent G actions on affine spaces for some finite and some connected semisimple groups. PMID:11607220
Mean Field Theory for Nonequilibrium Network Reconstruction
NASA Astrophysics Data System (ADS)
Roudi, Yasser; Hertz, John
2011-01-01
There has been recent progress on inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for nonequilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically coupled, synchronously updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one-time-step-delayed correlation functions.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
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 igΦ³ 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 gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Continuum regularization of quantum field theory
Bern, Z.
1986-01-01
Breit, Gupta, and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the fifth-time of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, difficulties arise which, in general, ruins the scheme. A successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest.
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy. PMID:26574206
Generalization of the theory of far-field caustics by the catastrophe theory.
Theocaris, P S; Michopoulos, J G
1982-03-15
To generalize the theory of far-field caustics, three theorems and several corollaries are presented in this paper. Using the law of reflection and catastrophe theory we have established conditions to predict caustic patterns in a 3-D space, which were created from the reflection of a light beam from an analytically known surface. The general theory was readily reduced to the already known cases of diffraction, indicating the validity of the general theory. Experimental evidence in two simple cases of reflectors, consisting of triangular and rectangular membranes, corroborated the results of the theory. PMID:20389809
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
Effective Field Theories from Soft Limits of Scattering Amplitudes.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist. PMID:26196613
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
Some equivalences between the auxiliary field method and envelope theory
Buisseret, Fabien; Semay, Claude; Silvestre-Brac, Bernard
2009-03-15
The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles a priori. This equivalence leads to a deeper understanding of both frameworks.
Hermeneutical Field Theory and the Structural Character of Understanding.
NASA Astrophysics Data System (ADS)
Whitehouse, William Leonard
Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints and degrees of freedom that constitute the structural character of understanding. However, as is sometimes the case with their quantitative mathematical counterparts, the hermeneutical field equations are capable of giving a variety of descriptions or solutions for one and the same set of conditions. The task, therefore, is to try to sort out those solutions which have reflective properties with respect to the structural character of reality from those which do not have such properties. The thesis addresses this task by introducing the idea of hermeneutical field theory. In this theory the notion of a semiotic operator or semiotic quantum plays a central role. More specifically, this quantum is considered to be the carrier of hermeneutical force. It arises as a field property at the complex, horizontal membrane-manifold linking human consciousness with different levels of scale of reality. When taken collectively, the aforementioned set of equations gives expression to the structural character of hermeneutical field theory. Therefore, when one begins to run concrete variables through the theory underlying these equations, one encounters various kinds of hermeneutical constraints and degrees of freedom. These constraints and degrees of freedom characterize the dialectical engagement of consciousness and reality as one seeks to acquire understanding concerning the above mentioned variables and the context which gives rise to them. Hermeneutical field theory is really the study of the factors that affect the state of the six internal
Post-measurement bipartite entanglement entropy in conformal field theories
NASA Astrophysics Data System (ADS)
Rajabpour, M. A.
2015-08-01
We derive exact formulas for bipartite von Neumann entanglement entropy after partial projective local measurement in (1 +1 ) -dimensional conformal field theories with periodic and open boundary conditions. After defining the setup we will check numerically the validity of our results in the case of Klein-Gordon field theory (coupled harmonic oscillators) and spin-1 /2 X X chain in a magnetic field. The agreement between analytical results and the numerical calculations is very good. We also find a lower bound for localizable entanglement in coupled harmonic oscillators.
Cold atom simulation of interacting relativistic quantum field theories.
Cirac, J Ignacio; Maraner, Paolo; Pachos, Jiannis K
2010-11-01
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations. PMID:21231152
Dualities among one-time field theories with spin, emerging from a unifying two-time field theory
Bars, Itzhak; Quelin, Guillaume
2008-06-15
The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS{sub d-k}xS{sup k}, and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
Dualities among one-time field theories with spin, emerging from a unifying two-time field theory
NASA Astrophysics Data System (ADS)
Bars, Itzhak; Quélin, Guillaume
2008-06-01
The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdSd-k×Sk, and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
Prime Numbers, Quantum Field Theory and the Goldbach Conjecture
NASA Astrophysics Data System (ADS)
Sanchis-Lozano, Miguel-Angel; Barbero G., J. Fernando; Navarro-Salas, José
2012-09-01
Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators bp\\dag — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
Quantum field theory constrains traversable wormhole geometries
Ford, L.H. |; Roman, T.A. |
1996-05-01
Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
Warped conformal field theory as lower spin gravity
NASA Astrophysics Data System (ADS)
Hofman, Diego M.; Rollier, Blaise
2015-08-01
Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.
A gauge field theory of fermionic continuous-spin particles
NASA Astrophysics Data System (ADS)
Bekaert, X.; Najafizadeh, M.; Setare, M. R.
2016-09-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Conformal field theory out of equilibrium: a review
NASA Astrophysics Data System (ADS)
Bernard, Denis; Doyon, Benjamin
2016-06-01
We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.
Red Galaxy Structures Toward a Large Quasar Group Field
NASA Astrophysics Data System (ADS)
Williger, Gerard M.; Feil, E. C.; Haberzettl, L.; Clowes, R.; Campusano, L.; Haines, C. P.; Valls-Gabaud, D.; Lehnert, M.; Nesvadba, N.; LQG Team
2014-01-01
We present data from deep FUV-NUV-griz images toward a 2 sq degree region in the Clowes-Campusano Large Quasar Group field, which contains structures of quasars on the >100 Mpc scale at 0.8 and 1.2. Large Quasar Groups may be the signal posts for galaxy structures analogous to superclusters at high redshift. Using the six band photometry, we calculate photometric redshifts for red-selected galaxies to identify supercluster-size structures, and compare their locations with the quasars in the field.
New method of applying conformal group to quantum fields
NASA Astrophysics Data System (ADS)
Han, Lei; Wang, Hai-Jun
2015-09-01
Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method (RGM). We start with the renormalization group equation (RGE), in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application, we find out that quite a few interaction vertices are separately invariant under certain transformations (generators) of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime. Supported by NSFC (91227114)
Renormalization Group Theory Technique and Subgrid Scale Closure for Fluid and Plasma Turbulence.
NASA Astrophysics Data System (ADS)
Zhou, Ye.
Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the epsilon - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite epsilon , but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.
More is the Same; Phase Transitions and Mean Field Theories
NASA Astrophysics Data System (ADS)
Kadanoff, Leo P.
2009-12-01
This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of "singularity", "order parameter", "mean field theory", "variational method", "correlation length", "universality class", "scale changes", and "renormalization". The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and
Effective field theories for QCD with rooted staggered fermions
Bernard, Claude; Golterman, Maarten; Shamir, Yigal
2008-04-01
Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the 'rooting trick' is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalization of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to 'rooted' staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-group based arguments for the correctness of the continuum limit and the success of rooted staggered chiral perturbation theory in fitting numerical results obtained with the rooting trick. In order to develop our argument, we need to assume the existence of a standard partially-quenched chiral effective theory for any local partially-quenched theory. Other technical, but standard, assumptions are also required.
Thermofield dynamics extension of the open string field theory
NASA Astrophysics Data System (ADS)
Botta Cantcheff, M.; Scherer Santos, R. J.
2016-03-01
We study the application of the rules of thermofield dynamics (TFD) to the covariant formulation of open-string field theory. We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended Becchi, Rouet, Stora and Tyutin (BRST) charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement, and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it of which the results at tree level agree with those of the conventional theory.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
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 igΦ³ quantum field theory. This quantum fieldmore » 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 gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
Effective Field Theories from Soft Limits of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
Consistent constraints on the Standard Model Effective Field Theory
NASA Astrophysics Data System (ADS)
Berthier, Laure; Trott, Michael
2016-02-01
We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S, T analysis is modified by the theory errors we include as an illustrative example.
Quantum field theories on algebraic curves. I. Additive bosons
NASA Astrophysics Data System (ADS)
Takhtajan, Leon A.
2013-04-01
Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.
Renormalization-group theory for the eddy viscosity in subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
Nonperturbative renormalization group approach for a scalar theory in higher-derivative gravity
Bonanno, A.; Zappala, D.
1997-05-01
A renormalization group study of a scalar theory coupled to gravity through a general functional dependence on the Ricci scalar in the action is discussed. A set of nonperturbative flow equations governing the evolution of the new interaction terms generated in both local potential and wave function renormalization is derived. It is shown for a specific model that these new terms play an important role in determining the scaling behavior of the system above the mass of the inflaton field. {copyright} {ital 1997} {ital The American Physical Society}
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Regularization methods for Nuclear Lattice Effective Field Theory
NASA Astrophysics Data System (ADS)
Klein, Nico; Lee, Dean; Liu, Weitao; Meißner, Ulf-G.
2015-07-01
We investigate Nuclear Lattice Effective Field Theory for the two-body system for several lattice spacings at lowest order in the pionless as well as in the pionful theory. We discuss issues of regularizations and predictions for the effective range expansion. In the pionless case, a simple Gaussian smearing allows to demonstrate lattice spacing independence over a wide range of lattice spacings. We show that regularization methods known from the continuum formulation are necessary as well as feasible for the pionful approach.
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Chiral Effective Field Theory in the $\\Delta$-resonance region
Vladimir Pascalutsa
2006-09-18
I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the $\\Delta(1232)$, the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the $\\Delta$-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Inductive approach towards a phenomenologically more satisfactory unififed field theory
Rayski, J.; Rayski J.M. Jnr.
1985-11-01
A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.
Super-Group Field Cosmology in Batalin-Vilkovisky Formulation
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2016-04-01
In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.
Super-Group Field Cosmology in Batalin-Vilkovisky Formulation
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2016-09-01
In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.
Negative-frequency modes in quantum field theory
NASA Astrophysics Data System (ADS)
Dickinson, Robert; Forshaw, Jeff; Millington, Peter
2015-07-01
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.
A Variational Statistical-Field Theory for Polar Liquid Mixtures
NASA Astrophysics Data System (ADS)
Zhuang, Bilin; Wang, Zhen-Gang
Using a variational field-theoretic approach, we derive a molecularly-based theory for polar liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy of mixing and the dielectric constant as functions of mixture composition. Using only the dielectric constants and the molar volumes of the pure liquid constituents, the theory evaluates the mixture dielectric constants in good agreement with the experimental values for a wide range of liquid mixtures, without using adjustable parameters. In addition, the theory predicts that liquids with similar dielectric constants and molar volumes dissolve well in each other, while sufficient disparity in these parameters result in phase separation. The calculated miscibility map on the dielectric constant-molar volume axes agrees well with known experimental observations for a large number of liquid pairs. Thus the theory provides a quantification for the well-known empirical ``like-dissolves-like'' rule. Bz acknowledges the A-STAR fellowship for the financial support.
Motion of small bodies in classical field theory
Gralla, Samuel E.
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles. PMID:24702348
Noncausal propagation in spin-0 theories with external field interactions
NASA Technical Reports Server (NTRS)
Guertin, R. F.; Wilson, T. L.
1977-01-01
The two-component Sakata-Taketani (ST) spin-0 theory and the single-component Klein-Gordon theory are obtained from the five-component Duffin-Kemmer-Petiau (DKP) theory with six types of external field interactions by means of a Peirce decomposition. Whereas the DKP equation manifests the covariance, the ST equation manifests the causal properties. In particular, the presence of noncausal wave propagation when there is coupling to a second-rank tensor field is apparent from the form of the ST equation, in which the coefficients of all the space derivatives depend on the external field. The results indicate that the causal properties of higher-spin equations should also be obvious when they are expressed in 2(2J + 1)-component Schroedinger form
BPS index and 4d N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Sakai, Kazuhiro
2016-07-01
We study the BPS index for the four-dimensional rank-one N = 2 superconformal field theories H 0 , H 1 , H 2 , E 6 , E 7 , E 8. We consider compactifications of the E-string theory on T 2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.
The Solar hep Process in Effective Field Theory
T.-S. Park; L. E. Marcucci; R. Schiavilla; M. Viviani; A. Kievsky; S. Rosati; K. Kubodera; D.-P. Min; M. Rho
2001-09-01
Using effective field theory, we calculate the S-factor for the hep process in a totally parameter-free formulation. The transition operators are organized according to chiral counting, and their matrix elements are evaluated using the realistic nuclear wave functions obtained in the Correlated-hyperspherical-harmonics method. Terms of up to next-to-next-to-next-to-leading order in heavy-baryon chiral perturbation theory are considered. Fixing the only parameter in the theory by fitting the tritium beta-decay rate, we predict the hep S-factor with accuracy better than {approx} 20%.
ERIC Educational Resources Information Center
O'Neil, James M.
1998-01-01
Relates Wade's and Gelso's Male Reference Group Dependence Theory to past and present literature in the new psychology of men. Points out the strengths of the ideas and data; reflects on where the theory needs more clarification and extension. (MKA)
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
Ydri, Badis
2010-10-31
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar {phi}{sup 4} field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at {theta} = 0 there must exist a novel fixed point at {theta} = {infinity} corresponding to the quartic hermitian matrix model.
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
NASA Astrophysics Data System (ADS)
Ydri, Badis
2010-10-01
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar φ4 field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at θ = 0 there must exist a novel fixed point at θ = ∞ corresponding to the quartic hermitian matrix model.
Exact renormalization group and loop variables: A background independent approach to string theory
NASA Astrophysics Data System (ADS)
Sathiapalan, B.
2015-11-01
This paper is a self-contained review of the loop variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and massive modes. This gives interacting equations of motion for the modes of the string. Loop variable techniques are used to obtain gauge invariant equations. Since this method is not tied to flat space-time or any particular background metric, it is manifestly background independent. The technique can be applied to both open and closed strings. Thus gauge invariant and generally covariant interacting equations of motion can be written for massive higher spin fields in arbitrary backgrounds. Some explicit examples are given.
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
When Group Membership Gets Personal: A Theory of Identity Fusion
ERIC Educational Resources Information Center
Swann, William B., Jr.; Jetten, Jolanda; Gomez, Angel; Whitehouse, Harvey; Bastian, Brock
2012-01-01
Identity fusion is a relatively unexplored form of alignment with groups that entails a visceral feeling of oneness with the group. This feeling is associated with unusually porous, highly permeable borders between the personal and social self. These porous borders encourage people to channel their personal agency into group behavior, raising the…
Overcoming Denial through the Group: A Test of Acceptance Theory.
ERIC Educational Resources Information Center
Rugel, Robert P.; Barry, Denise
1990-01-01
Found participants (N=28) in alcohol treatment groups showed decreases in denial of drinking problems and decreases in psychopathology following 12 weeks of group counseling. Determined greater self-acceptance was associated with experiencing acceptance by group and with greater decreases in denial; decreases in denial and psychopathology were…
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories. PMID:27494465
Modular Hamiltonian for Excited States in Conformal Field Theory
NASA Astrophysics Data System (ADS)
Lashkari, Nima
2016-07-01
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Zn replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Closed string cohomology in open string field theory
NASA Astrophysics Data System (ADS)
Moeller, Nicolas; Sachs, Ivo
2011-07-01
We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten's 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.
Contour-ordered Green's functions in stochastic field theory
NASA Astrophysics Data System (ADS)
Honkonen, J.
2013-06-01
We briefly review the functional formulation of the perturbation theory for various Green's functions in quantum field theory. In particular, we discuss the contour-ordered representation of Green's functions at a finite temperature. We show that the perturbation expansion of time-dependent Green's functions at a finite temperature can be constructed using the standard Wick rules in the functional form without introducing complex time and evolution backward in time. We discuss the factorization problem for the corresponding functional integral. We construct the Green's functions of the solution of stochastic differential equations in the Schwinger-Keldysh form with a functional-integral representation with explicitly intertwined physical and auxiliary fields.
Negative contributions to S in an effective field theory
Dobrescu, Bogdan A.; Terning, John
1997-09-19
We show that an effective field theory that includes non-standard couplings between the electroweak gauge bosons and the top and bottom quarks may yield negative contributions to both the S and T oblique radiative electroweak parameters. We find that such an effective field theory provides a better fit to data than the standard model (the {chi}{sup 2} per degree of freedom is half as large). We examine in some detail an illustrative model where the exchange of heavy scalars produces the correct type of non-standard couplings.
Approaches to the sign problem in lattice field theory
NASA Astrophysics Data System (ADS)
Gattringer, Christof; Langfeld, Kurt
2016-08-01
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focusing on two more recent methods: dualization to worldline type of representations and the density-of-states approach.
Quantum field theory with a preferred direction: The very special relativity framework
NASA Astrophysics Data System (ADS)
Lee, Cheng-Yang
2016-02-01
The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group I S I M (2 ), we present a rigorous construction of quantum field theory with a preferred direction. We find that although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations, respectively. This result can be generalized to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarized processes but are otherwise absent.
A field theory of piezoelectric media containing dislocations
Taupin, V. Fressengeas, C.; Ventura, P.; Lebyodkin, M.
2014-04-14
A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.
Collapse transition of randomly branched polymers: renormalized field theory.
Janssen, Hans-Karl; Stenull, Olaf
2011-05-01
We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well-established dimensional-reduction results from a different angle. For the collapse θ transition, we uncover a hidden Becchi-Rouet-Stora supersymmetry, signaling the sole relevance of tree configurations. We correct the long-standing one-loop results for the critical exponents, and we push these results on to two-loop order. For the collapse θ' transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions. PMID:21728509
A field theory approach to the dynamics of classical particles
NASA Astrophysics Data System (ADS)
McCowan, David; Mazenko, Gene
2012-02-01
For nearly 30 years, mode-coupling theory (MCT) has been regarded as the de facto theoretic description of dense fluids and the transition from the fluid to glassy state. But MCT is limited by its ad hoc construction and lacks a mechanism to institute corrections. We present a new fundamental theory for the kinetics of systems of classical particles which represents a unification of kinetic theory, Brownian motion and field theory. It is developed from first principles via a self-consistent perturbation in terms of an effective two-body potential, and we use this theory to investigate the existence of ergodic-nonergodic (ENE) transitions near the liquid-glass transition. After a brief introduction of the theory, we will address the development of a kinetic equation of the memory function form. The memory function kernel (or self-energy) determined by the theory shares properties with the MCT form, however our theory provides the crucial advantage of well-defined, perturbative corrections.
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
N=2, 4 supersymmetric gauge field theory in two-time physics
Bars, Itzhak; Kuo, Y.-C.
2009-01-15
In the context of two-time physics in 4+2 dimensions we construct the most general N=2, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. When the equations of motion are used the SUSY transformations close to the supergroup SU(2,2|N) with N=1, 2, 4. The SU(2,2)=SO(4,2) subsymmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat 3+1 dimensions coincide with the well known counterpart N=1, 2, 4 supersymmetric massless renormalizable field theories in 3+1 dimensions. It is expected that our more symmetric new structures in 4+2 spacetime may be useful for nonperturbative or exact solutions of these theories.
Dualities between semiclassical strings and quantum gauge field theories
NASA Astrophysics Data System (ADS)
Ouyang, Peter
In this thesis we study several examples of the correspondence between gauge field theories and string theories. A recurrent theme of these studies is that distinctively quantum mechanical behavior on the gauge theory side of the correspondence can have a classical or semiclassical description in terms of string calculations, as one might expect from general considerations of open/closed duality. We begin in Chapter 1 by reviewing the simplest duality, which relates Type IIB supergravity in AdS5 x S5 to N = 4 SU(N) gauge theory at large N. Working with this background spacetirne, we turn to a study of D-brane probes with large quantum numbers in Chapter 2. We employ semiclassical methods to compute the excitation spectrum of these D-branes, including corrections of order 1/N, which are related to loop effects in the dual field theory. In Chapter 3 we discuss the gauge/gravity duals with N = 1 supersymmetry which arise from placing D-branes at a conifold singularity. The inclusion of fractional D3-branes breaks conformal invariance, leading to a rich variety of phenomena in the gauge theory, among them chiral anomalies, a cascade of Seiberg dualities and confinement in the infrared. We pay particular attention to the chiral anomalies of the gauge theory and show that they can be described in terms of classical spontaneous symmetry breaking in the dual string theory. In accord with low-energy confinement in the field theory, almost all of the moduli of the supergravity solution are fixed; we conclude Chapter 3 with some observations on the possibility of stabilizing the volume of the compact space in which the conifold is embedded. Finally, in Chapter 4 we study versions of the conifold theory with D7-branes, which introduce fundamental matter into the gauge theory. By solving the classical supergravity equations of motion we identify a variant of the Klebanov-Strassler duality cascade where the rate of the cascade decreases as the theory flows to low energies.
Velocity-Field Theory, Boltzmann's Transport Equation and Geometry
NASA Astrophysics Data System (ADS)
Ichinose, Shoichi
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.
When group membership gets personal: a theory of identity fusion.
Swann, William B; Jetten, Jolanda; Gómez, Angel; Whitehouse, Harvey; Bastian, Brock
2012-07-01
Identity fusion is a relatively unexplored form of alignment with groups that entails a visceral feeling of oneness with the group. This feeling is associated with unusually porous, highly permeable borders between the personal and social self. These porous borders encourage people to channel their personal agency into group behavior, raising the possibility that the personal and social self will combine synergistically to motivate pro-group behavior. Furthermore, the strong personal as well as social identities possessed by highly fused persons cause them to recognize other group members not merely as members of the group but also as unique individuals, prompting the development of strong relational as well as collective ties within the group. In local fusion, people develop relational ties to members of relatively small groups (e.g., families or work teams) with whom they have personal relationships. In extended fusion, people project relational ties onto relatively large collectives composed of many individuals with whom they may have no personal relationships. The research literature indicates that measures of fusion are exceptionally strong predictors of extreme pro-group behavior. Moreover, fusion effects are amplified by augmenting individual agency, either directly (by increasing physiological arousal) or indirectly (by activating personal or social identities). The effects of fusion on pro-group actions are mediated by perceptions of arousal and invulnerability. Possible causes of identity fusion--ranging from relatively distal, evolutionary, and cultural influences to more proximal, contextual influences--are discussed. Finally, implications and future directions are considered. PMID:22642548
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Finding Galaxy Groups in the Fields of Lensed Quasars
NASA Astrophysics Data System (ADS)
Grant, Catherine E.; Bautz, M. W.
2006-09-01
Gravitationally lensed quasars can be used as an invaluable cosmological tool, however, the asymmetry observed in many lensed systems requires models of the lens to include a strong external shear component in addition to the lensing galaxy. The lensing galaxy may be a member of a group or cluster which could provide sufficient shear to account for the lensed image configuration. We are searching for X-ray emission from groups and clusters of galaxies in the fields of multiply-imaged quasars using Chandra's resolving power to separate the faint diffuse emission from the much brighter quasar images. We have analyzed all observations of gravitationally lensed quasars available in the Chandra archive from launch through the end of 2005 to search for this diffuse emission. We present a catalog of cluster and group properties for those fields with significant diffuse emission, and upper limits on group properties in fields where no diffuse emission is detected. These measurements are compared with optical data, where available, and with quasar lensing models. This research was supported by NASA contracts NAS-8-38252 and NAS-8-37716.
Empirical research on attachment in group psychotherapy: moving the field forward.
Marmarosh, Cheri L
2014-03-01
Despite a large literature applying attachment to individual, family, and couple psychotherapy, it has taken much longer for clinicians to apply attachment theory to group psychotherapy. The lack of research attention in this area makes these three studies in this special section even more important to the field. They contribute significant findings that have the potential to help group leaders facilitate more cohesive and effective treatments for patients as well as move the field forward. Not only do we see the long-term impact of group treatment for those with insecure attachments, but we also learn how attachment anxiety impacts the group process, and how the attachment to the therapy group itself relates to changes in group member's personal attachment styles. The greatest contribution is the drawing of our attention to the many future studies that are needed to fully understand how group therapy facilitates change and how attachment theory plays a critical role in this process. Clinical implications are presented. PMID:24059737
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
NASA Astrophysics Data System (ADS)
Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, René; Park, Jeong-Hyuck
2015-12-01
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations.
An effective field theory for forward scattering and factorization violation
NASA Astrophysics Data System (ADS)
Rothstein, Ira Z.; Stewart, Iain W.
2016-08-01
Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where | t| ≪ s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude's rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to
Theory of cyclotron super-radiance from a moving electron bunch under group synchronism condition
NASA Astrophysics Data System (ADS)
Ginzburg, N. S.; Zotova, I. V.; Sergeev, A. S.; Rozental, R. M.; Phelps, A. D. R.; Cross, A. W.; Ronald, K.
2003-11-01
A theory of cyclotron super-radiance (SR) from a moving electron bunch under a group synchronism condition has been developed. This regime occurs for the propagation of a radiation field in a waveguide or in other dispersive media such as a plasma when the electron bunch translational velocity coincides with the wave group velocity. In the comoving reference frame such emission corresponds to emission at a quasi-cut-off frequency. For a linear approximation it is shown that a bunch of electrons rotating in the magnetic field can be presented as an active resonator which possesses a spectrum of unstable eigenmodes. The gain of these modes defines the gain of the SR instability. To describe the nonlinear stage of the SR instability a time-domain approach based on a combination of a parabolic equation for wave evolution and a non-isochronous oscillator equation to describe electron azimuthal self-bunching was used. Profiles of SR pulses were found first in the comoving reference frame and then transferred into the laboratory reference frame using a Lorentz transformation. Both linear and nonlinear analyses demonstrated the advantage of SR in the regime of group synchronism as compared to cyclotron SR in free space. The fast drop of the SR pulse amplitude by detuning the magnetic field from the grazing condition was observed using the three-dimensional particle-in-cell code KARAT.
Tushev, A V
2006-10-31
In the present paper certain methods are developed that enable one to study the properties of the controller of a prime faithful ideal I of the group algebra kA of an Abelian torsion-free group A of finite rank over a field k. The main idea is that the quotient ring kA/I by the given ideal I can be embedded as an integral domain k[A] into some field F and the group A becomes a subgroup of the multiplicative group of the field F. This allows one to apply certain results of field theory, such as Kummer's theory and the properties of the multiplicative groups of fields, to the study of the integral domain k[A]. In turn, the properties of the integral domain k[A]{approx_equal}kA/I depend essentially on the properties of the ideal I. In particular, by using these methods, an independent proof of the new version of Brookes's theorem on the controllers of prime ideals of the group algebra kA of an Abelian torsion-free group A of finite rank is obtained in the case where the field k has positive characteristic.
Positive Energy Conditions in 4D Conformal Field Theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus; Prilepina, Valentina
2016-03-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality avgT00 >= - C /L4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the ``conformal collider'' constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
Tensor Networks for Lattice Gauge Theories with Continuous Groups
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Lewenstein, M.
2014-10-01
We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
Theories in Developing Oral Communication for Specific Learner Group
ERIC Educational Resources Information Center
Hadi, Marham Jupri
2016-01-01
The current article presents some key theories most relevant to the development of oral communication skills in an Indonesian senior high school. Critical analysis on the learners' background is employed to figure out their strengths and weaknesses. The brief overview of the learning context and learners' characteristic are used to identify which…
Testing Belbin's Team Role Theory of Effective Groups.
ERIC Educational Resources Information Center
Prichard, Jane S.; Stanton, Neville A.
1999-01-01
Belbin's theory that teams with a wide range of roles are more effective than those with role imbalance was tested with six teams composed of individuals with homogenous roles and six with mixed roles. Mixed teams performed better on team tasks. (SK)
Unified theory of near-field analysis and measurement - Scattering and inverse scattering
NASA Astrophysics Data System (ADS)
Wacker, P. F.
1981-03-01
The scanning procedures of unified theory of near-field analysis and measurement are adapted to the determination of scattering patterns of electromagnetic and scalar systems from measurements made in the near, intermediate, or far field, with emphasis on high accuracy and efficient data processing. The scanning procedures include spherical, improved plane polar, and many types of plane rectangular, plane radial, and circular cylindrical scanning. Application of group representation to inverse scattering analysis is discussed.
The Effective Field Theory Approach to Fluid Dynamics
NASA Astrophysics Data System (ADS)
Endlich, Solomon George Shamsuddin Osman
In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
On gradient field theories: gradient magnetostatics and gradient elasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2014-09-01
In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot-Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach-Koehler stress equation, Peach-Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Field-Based Concerns about Fourth-Generation Evaluation Theory.
ERIC Educational Resources Information Center
Lai, Morris K.
Some aspects of fourth generation evaluation procedures that have been advocated by E. G. Guba and Y. S. Lincoln were examined empirically, with emphasis on areas where there have been discrepancies between theory and field-based experience. In fourth generation evaluation, the product of an evaluation is not a set of conclusions, recommendations,…
Sketch of J. R. Kantor's Psychological Interbehavioral Field Theory
ERIC Educational Resources Information Center
Delprato, Dennis J.; Smith, Noel W.
2009-01-01
We provide a sketch of J. R. Kantor's (1959, 1971) psychological interbehavioral field (IBF) theory by identifying 9 essential points and briefly discussing each. The main emphasis of this sketch is on the foundation of Kantor's thinking, the IBF. Suggestions for further study are provided.
The effective field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg00(u))n at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
Approximate Near-Field Blast Theory: A Generalized Approach
Hutchens, G.J.
1999-10-25
A method for analyzing strong shock waves in arbitrary one-dimensional geometry is presented. An approximation to classical Taylor-Sedov theory is extended to the near-field case where source mass is not negligible, accounting for differences in the chemical properties of the source mass and ambient medium. Results from example calculations are compared with previously published analytical formulae.
Schr"odinger's Unified Field Theory: Physics by Public Relations
NASA Astrophysics Data System (ADS)
Halpern, Paul
2009-05-01
We will explore the circumstances surrounding Erwin Schr"odinger's announcement in January 1947 that he had developed a comprehensive unified field theory of gravitation and electromagnetism. We will speculate on Schr"odinger's motivations for the mode and tone of his statements, consider the reaction of the international press within the context of the postwar era, and examine Einstein's response.
Holography and hydrodynamics for EMD theory with two Maxwell fields
NASA Astrophysics Data System (ADS)
Smolic, Milena
2013-03-01
We use `generalized dimensional reduction' to relate a specific Einstein-Max-well-Dilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higher-dimensional AdS gravity (with no higher-dimensional Maxwell field). In general, this is a dimensional reduction over compact Einstein spaces in which the dimension of the compact space is continued to non-integral values. Specifically, we perform a non-diagonal Kaluza-Klein (KK) reduction over a torus, involving two KK gauge fields. Our aim is to determine the holographic dictionary and hydrodynamic behaviour of the lower-dimensional theory by performing the generalized dimensional reduction on AdS. We study a specific example of a black brane carrying a wave, whose universal sector is described by gravity coupled to two Maxwell fields, three neutral scalars and an axion, and compute the first order transport coefficients of the dual theory. In these theories {{widehat{ζ}}_s}/widehat{η}<2( {1/( {d-1} )-widehat{c}_s^2} ) , where {{widehat{c}}_s} is the speed of sound, violating a conjectured bound, but an alternative bound is satisfied.
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Chiral field theories as models for hadron substructure
Kahana, S.H.
1987-03-01
A model for the nucleon as soliton of quarks interacting with classical meson fields is described. The theory, based on the linear sigma model, is renormalizable and capable of including sea quarks straightforwardly. Application to nuclear matter is made in a Wigner-Seitz approximation.
Probing {N}=2 superconformal field theories with localization
NASA Astrophysics Data System (ADS)
Fiol, Bartomeu; Garolera, Blai; Torrentsa, Genís
2016-01-01
We use supersymmetric localization to study probes of four dimensional Lagrangian {N}=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of {N}=4 supersymmetric Yang-Mills theory.
Field theory as a tool to constrain new physics models
NASA Astrophysics Data System (ADS)
Maas, Axel
2015-08-01
One of the major problems in developing new physics scenarios is that very often the parameters can be adjusted such that in perturbation theory almost all experimental low-energy results can be accommodated. It is therefore desirable to have additional constraints. Field-theoretical considerations can provide such additional constraints on the low-lying spectrum and multiplicities of models. Especially for theories with elementary or composite Higgs particle the Fröhlich-Morchio-Strocchi (FMS) mechanism provides a route to create additional conditions, though showing it to be at work requires genuine non-perturbative calculations. The qualitative features of this procedure are discussed for generic 2-Higgs-doublet models (2HDMs), grand-unified theories (GUTs) and technicolor-type theories.