Proof of chiral symmetry breaking in strongly coupled lattice gauge theory

We study chiral symmetry in the strong coupling limit of lattice gauge theory with staggered fermions and show rigorously that chiral symmetry is broken spontaneously in massless QED and the gauge-invariant Nambu-Jona-Lasinio model if the dimension of spacetime is at least four. The results for the chiral condensate as a function of the mass imply that the mean-field approximation is an upper bound for this observable which becomes exact as the dimension goes to infinity. For the model with gauge groupU(N),N=2,3,4, we prove that chiral long-range order exists at zero mass in four or more dimensions. Address after August 1991: Mathematics Department, University of British Columbia, Vancouver, Canada V6T1Y4     

The Relation Between Gauge and Non-Gauge Abelian Models

This work studies the relationship between gauge-invariant and non gauge-invariant Abelian vector models. Following a technique introduced by Harada and Tsutsui, we show that the Proca and the chiral Schwinger models may both be viewed as gauge-fixed versions of genuinely gauge-invariant models. This leads to the proposal that any consistent Abelian vector model with no gauge symmetry can be understood as a gauge theory that had its gauge fixed, which establishes an equivalence between gauge-invariant and non gauge-invariant models. Finally, we show that a gauge-invariant version of the chiral Schwinger model, after integrating out the fermionic degrees of freedom, can be identified with the two-dimensional Stueckelberg model without the gauge-fixing term.     

Chiral Bosonized Versions Hidden in Chiral Schwinger Models

The left- and right-handed chiral Schwinger models are re-examined by a modified chiral bosonization. Contrary to the usual chiral bosonization, we impose the chiral constraint on the right-handed chiral Schwinger model and the antichiral constraint on the left-handed one. The resulting chiral boson and theories are gauge-invariant and equivalent to one (free) cbiral boson and one antichiral boson respectively.     

A gauge-invariant chiral unitary framework for kaon photo- and electroproduction on the proton

We present a gauge-invariant approach to photoproduction of mesons on nucleons within a chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. Within the leading-order approximation to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and CBELSA/TAPS are analyzed in the threshold region. The importance of gauge invariance and the precision of various approximations in the interaction kernel utilized in earlier works are discussed.     

Tumbling in two-dimensional gauge theories

The ideas of tumbling and most attractive channel condensation are confronted in two-dimensional chiral gauge theories. We first demonstrate how to perform a gauge-invariant regularization. We then proceed to find exact results about the spectra in both abelian and non-abelian cases. These conflict with the predictions of tumbling and MAC.     

η-Photoproduction in a gauge-invariant chiral unitary framework

We analyze photoproduction of η mesons off the proton in a gauge-invariant chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the leading order chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. The recent precise threshold data from the Crystal Ball at MAMI can be described rather well and the complex pole corresponding to the S₁₁(1535) is extracted. An extension of the kernel is also discussed.     

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.     

On a construction of self-dual gauge fields in seven dimensions

Abstract

We consider gauge fields associated with a semisimple Malcev algebra. We construct a gauge-invariant Lagrangian and found a solution of modified Yang-Mills equations in seven dimensions.     

A gauge-invariant theory of chiral bosons: Wess-Zumino term,Hamiltonian and BRST formulations

The Wess-Zumino term for the gauge-non-invariant Srivastava model for single self-dual chiral bosons is constructed, and the Hamiltonian and BRST formulations of the resulting gauge-invariant theory (obtained by the inclusion of the Wess-Zumino term) are investigated.     

BFV Quantization of the Minimal Chiral Schwinger Model

Both the gauge-invariant and the gaugenoninvariant versions of the minimal chiral Schwinger model are quantized by using the BFV formalism for the two cases of the regularization'parameter a > 1 and a = 1. The equivalence of these two versions of the model is then established in a gauge-independent manner.     

A note on unparticle in lower dimensions

Using the gauge-invariant but path-dependent variables formalism, we examine the effect of the space–time dimensionality on a physical observable in the unparticle scenario. We explicitly show that long-range forces between particles mediated by unparticles are still present whenever we go over into lower dimensions.     

Yang-Mills theory in three dimensions as a quantum gravity theory

We perform the dual transformation of theYang-Mills theory in three dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but which is embedded into a flat 6-dimensional space [for the SU(2) gauge group]. In the continuum limit, the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual-color space. The Yang-Mills theory can also be rewritten as a quantum gravity theory with the Einstein-Hilbert action but with a purely imaginary Newton constant plus a homogeneous “ether” term. The theory can be formulated in a gauge-invariant and local form without explicit color degrees of freedom.     

Consistent massive anomalous dimensions

We re-evaluate the O(g²) momentum-subtracted anomalous dimensions of QCD with massive quarks. The QCD equations of motion are used to relate operator matrix elements with different tensor structures. This procedure yields explicitly gauge-invariant anomalous dimensions. Our results differ slightly from those in the literature. The forward Compton amplitude for scattering of massive quarks and a scalar current is examined. The large Q² behavior of this amplitude is shown to be simply related to the momentum-subtracted, mass-dependent anomalous dimension.     

Quantization of Two Classical Models by Means of the BRST Quantization Method

An elementary gauge-non-invariant model and the bosonized form of the chiral Schwinger model are introduced as classical theories. The constraint structure is then investigated. It is shown that by introducing a new field, these models can be made gauge-invariant. The BRST form of quantization is reviewed and applied to each of these models in turn such that gauge-invariance is not broken. Some consequences of this form of quantization are discussed.     

Gauge-invariant correlation functions for the Ising-gauge Ising-Higgs system in 2 dimensions

We use recent calculations of correlation functions of the 2-dimensional Ising model in the presence of a magnetic field to study the Z₂-gauge Z₂-Higgs system in 2 dimensions. We study both the correlation of two plaquettes and the gauge-invariant correlation of Higgs fields. From these we are able to discuss criteria for confinement in the presence of matter.     

Determination of Phase Space Spectra of the Generalized Chiral Schwinger model with the Lorentz invariant Mass like Term for the Choice a − r2 = 0

We have considered the generalized version of chiral schwinger model with the Lorentz covariant masslike term for gauge field with the choice a ? r² =?0. We carry out the quantization by the canonical Dirac method of both the gauge-invariant and non-invariant version of this model to determine the phase space structure. Therefore we have shown that the gauge invariant theory has the same physical spectrum as that of the original gauge noninvariant formulation.

     

Color anomaly and flavor-singlet axial charge of the proton in the chiral bag: The Cheshire Cat revisited

Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the “proton spin problem” on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading order in the color gauge coupling and for a specific color electric monopole configuration in the bag, one can obtain a striking Cheshire-Cat phenomenon with a negligibly small singlet axial charge.     

A relation between gauge-invariant formulation of QCD and string theory in two dimensions

We have studied the explicit relation between the gauge-invariant path-ordered operator (POO) and a string field in two dimensions. For this purpose, we use the hamiltonian of two-dimensional quantum chromodynamics reformulated in terms of POO. POO is expanded in a power series of a non-local bosonic operator. We show that such a bosonic operator describes Bars and Hanson's free string field in the second quantization. Interactions among bosonic operators are treated in perturbation theory. The coupling constant is proportional to 1/√N_c.     

Planar Yang-Mills theory: Hamiltonian,regulators and mass gap

We carry out the Hamiltonian analysis of non-Abelian gauge theories in (2+1) dimensions in a gauge-invariant matrix parametrization of the fields. A detailed discussion of regularization issues and the construction of the renormalized Laplace operator on the configuration space, which is proportional to the kinetic energy, are given. The origin of the mass gap is analyzed and the lowest eigenstates of the kinetic energy are explicitly obtained; these have zero charge and exhibit a mass gap. The nature of the corrections due to the potential energy, the possibility of an improved perturbation theory and a Schrödinger-like equation for the states are also discussed.     

Spinor electrodynamics in terms of gauge-invariant quantities

We give a formulation of classical spinor electrodynamics in terms of gauge-invariant quantities. The set of invariants consists of bilinear combinations of spinor fields (currents), a real-valued covector field, and a complex scalar field of modulus one. The presented result is a first step towards formulating quantum electrodynamics in terms of gauge-invariant fields.