Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.     

Constituent quarks from QCD

Starting from the observation that colour charge is only well defined on gauge invariant states, we construct perturbatively gauge invariant, dynamical dressings for individual quarks. Explicit calculations show that an infra-red finite mass-shell renormalisation of the gauge invariant, dressed propagator is possible and, further, that operator product effects, which generate a running mass, may be included in a gauge invariant way in the propagator. We explain how these fields may be combined to form hadrons and show how the interquark potential can now be directly calculated. The onset of confinement is identified with an obstruction to building a non-perturbative dressing. We propose several methods to extract the hadronic scale from the interquark potential. Various extensions are discussed.     

Nonperturbative dynamics of noncommutative gauge theory

We present a nonperturbative lattice formulation of noncommutative Yang–Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with p·n_f flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n_f species of matter on a lattice of size p·L with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.     

Representations of Canonical Commutation Relations Describing Infinite Coherent States

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.     

Renormalization and asymptotic behavior in a finite quantum field theory with shadow states

In this paper we present a study of the renormalization problem in a finite quantum field theory with shadow states for a system of a physical scalar field interacting with a physical fermion field. In order to make the theory finite, two fermion shadow fields are introduced. We observe that the stability criterion of renormalization can not be satisfied simultaneously by both physical fields and shadow fields, if the finiteness of the theory is to be maintained. A physical interpretation of this result is given. Furthermore, we find that the effective complete propagators for large space-like momenta behave like free field propagators without the logarithmic factors observed in the non-abelian gauge theory.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

高阶微商系统中正则Ward恒等式和Abel规范理论中动力学质量的产生

基于含复合场的正则Ward恒等式，研究了含高阶微商的Abel理论中动力学规范对称破缺.得到了包括费米子和束缚态的质量谱.讨论了高阶微商项的影响. 关键词： 正则Ward恒等式 约束 动力学对称破缺 Abel规范理论     

Quantum gauge equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb, and spatial axial gauges to what we call “common form,” in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.     

The Hadamard Condition for Dirac Fields and Adiabatic States on Robertson–Walker Spacetimes

We characterise the homogeneous and isotropic gauge invariant and quasifree states for free Dirac quantum fields on Robertson–Walker spacetimes. Using this characterisation, we construct adiabatic vacuum states of order n corresponding to some Cauchy surface. It is demonstrated that any two such states (of sufficiently high order) are locally quasi-equivalent. We give a microlocal characterisation of spinor Hadamard states and we show that this agrees with the usual characterisation of such states in terms of the singular behaviour of their associated twopoint functions. The polarisation set of these twopoint functions is determined and found to have a natural geometric form. We finally prove that our adiabatic states of infinite order are Hadamard, and that those of order n correspond, in some sense, to a truncated Hadamard series and therefore allow for a point splitting renormalisation of the expected stress-energy tensor. Received: 30 June 1999 / Accepted: 21 September 2000     

Ground states of Fermions on lattices

We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).     

HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow

We first construct an approximate Riemann solver of the HLLC-type for the Baer–Nunziato equations of compressible two-phase flow for the “subsonic” wave configuration. The solver is fully nonlinear. It is also complete, that is, it contains all the characteristic fields present in the exact solution of the Riemann problem. In particular, stationary contact waves are resolved exactly. We then implement and test a new upwind variant of the path-conservative approach; such schemes are suitable for solving numerically nonconservative systems. Finally, we use locally the new HLLC solver for the Baer–Nunziato equations in the framework of finite volume, discontinuous Galerkin finite element and path-conservative schemes. We systematically assess the solver on a series of carefully chosen test problems.     

Finite Groups and Quantum Yang–Baxter Equations

We construct integrable modifications of two-dimensional lattice gauge theories with finite gauge groups.     

Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions

We develop the BRST approach to Lagrangian formulation for massive higher integer spin fields on a flat space–time of arbitrary dimension. General procedure of gauge invariant Lagrangian construction describing the dynamics of massive bosonic field with any spin is given. No off-shell constraints on the fields (like tracelessness) and the gauge parameters are imposed. The procedure is based on construction of new representation for the closed algebra generated by the constraints defining an irreducible massive bosonic representation of the Poincaré group. We also construct Lagrangian describing propagation of all massive bosonic fields simultaneously. As an example of the general procedure, we derive the Lagrangians for spin-1, spin-2 and spin-3 fields containing total set of auxiliary fields and gauge symmetries of free massive bosonic higher spin field theory.     

Infrared regularization of superstring theory and the one-loop calculation of coupling constants

Infrared regularized versions of 4-D N = 1 superstring ground states are constructed by curving the spacetime. A similar regularization can be performed in field theory. For the IR regularized string ground states we derive the exact one-loop effective action for non-zero U(1) or chromomagnetic fields as well as gravitational and axionic-dilatonic fields. This effective action is IR and UV finite. Thus, the one-loop corrections to all couplings (gravitational, gauge and Yukawas) are unambiguously computed. These corrections are necessary for quantitative string superunification predictions at low energies. The one-loop corrections to the couplings are also found to satisfy Infrared Flow Equations.     

S-duality of color-ordered amplitudes

Recently, it has been proposed that the S-matrix elements on the world volume of an abelian D₃-brane are consistent with the Ward identity associated with the S-duality. In this paper we extend this study to the case of multiple D₃-branes. We speculate that the S-matrix elements are consistent with the S-dual Ward identity irrespective of the ordering of the external states. Imposing this symmetry on the particular case of the S-matrix element of one Kalb–Ramond, one transverse scalar and two non-abelian gauge bosons, we will find the linear S-duality transformation of the commutator of two non-abelian gauge field strengths. Using this transformation and the standard S-duality transformations of the supergravity fields, all other non-abelian S-matrix elements of one closed and three open string states can be found by the S-duality proposal. We will show that the predicted S-matrix elements are reproduced exactly by explicit calculations.     

Wilson loops and constant gauge fields

We have computed the Wilson loop averaged over the class of constants gauge fields in two dimensions forSU(N), withN large. The limitN→∞ gives asymptotically an “area law” when the area of the loop tends to the total finite volume of space.     

Critical dynamics of superconductors in the charged regime

We investigate the finite temperature critical dynamics of three-dimensional superconductors in the charged regime, described by a transverse gauge field coupling to the superconducting order parameter. Assuming relaxational dynamics for both the order parameter and the gauge fields, within a dynamical renormalization group scheme, we find a new dynamic universality class characterized by a finite fixed point ratio between the transport coefficients associated with the order parameter and gauge fields, respectively. We find signatures of this universality class in various measurable physical quantities, and in the existence of a universal amplitude ratio formed by a combination of physical quantities.     

Finite size effects and spontaneously broken symmetries: the case of theO(4) model

Finite volume numerical simulations of scalar models with continuous symmetry face strong finite size effects in the broken phase due to the presence of light Goldstone states. In the region where the light Goldstone bosons dominate the dynamics of the system universal finite size scaling formulae are predicted by chiral perturbation theory. Introducing a finite external source one can determine infinite volume, zero external source physical quantities from finite volume observables. Here we apply this theoretically controlled approach to the 4 dimensionalO(4) scalar model. All of our numerical results are in excellent agreement with the predicted finite size scaling forms. We confirm earlier results at zero external source where the infinite volume limit was approximated by projecting the fields to the direction of the magnetization.     

The effect of a topological gauge field on Bose–Einstein condensation

We show that Bose–Einstein condensation of charged scalar fields interacting with a topological gauge field at finite temperature is inhibited except for special values of the topological field. We also show that fermions interacting with this topological gauge field can condense for some values of the gauge field.