A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)

We describe a non-perturbative study of the infrared behavior of the axial gauge gluon propagator based on the Dyson equation and Ward identities. We conclude that the propagator Δ_μν(q) displays a q^?4 singularity in the infrared limit, and that consequently the axial gauge running coupling constant g_A²)(q) displays a q^?2 singularity in the same limit. The only assumption necessary to obtain this conclusion is that the transverse part of the triple-gluon vertex function does not dominate the longitudinal part in the infrared regime.     

Infrared properties of the glue propagator in non-abelian gauge theories

In a pure Yang-Mills theory, the Dyson equation for the gluon propagator is studied in the infrared regime, under the assumption that, as in QED, only those parts of the proper gluon vertex functions determined by the Ward identities are relevant. The calculations are all carried out in the axial gauge. With a number of simplifying assumptions the resulting integral equation for the gluon propagator can be solved in the IR regime. The solution displays a power singularity in the IR for the renormalized coupling constant g(q²).     

Regge behavior under asymptotic freedom

By a new method, we show that the asymptotically free ø₆³ field theory has a point of accumulation of Regge poles but no fixed cut. It is plausible that nonabelian gauge theories have an analogous singularity at j = 1.     

An analytic calculation of the weak field limit of the static color dielectric constant

We analyze the Dyson equation/Ward identity system for the axial gauge n · A = 0 gluon propagator Δ_μν(q)whenn · q = 0. The solution behaves like (q^?4 + (q²)^ν?1) for small q₂, and we are able to calculate the power ν analytically. It turns out to be 0.1737. This analytic calculation verifies our earlier numerical solutions to these equations. For static problems, n · q = 0 is the temporal gauge, and in this gauge the gluon propagator is directly related to the color dielectric constant. We can thus calculate the dielectric constant in the infrared limit.     

High precision mean-field results for lattice gauge theories: with special attention paid to the gauge dependence of mean-field perturbation theory to finite order

We do mean-field perturbation theory for U(1) lattice gauge theory in the axial gauge, and evaluate corrections from fluctuations up to fourth order for the free energy and plaquette energy. Comparing with similar results previously obtained in the Feynman gauge we find, to those orders studied, a gauge dependence of the size of the first correction term neglected with one exception. This gauge dependence decreases rapidly as the order of the approximation is increased. To any finite order, results in axial gauge are better approximations than results in the Feynman gauge. We speculate why. Assuming it to be generally true, we evaluate the first correction beyond the one-loop mean-field approximation to the free energy of SU(2) gauge theory with Wilson action in the axial gauge. This correction brings the mean-field result very close to Monte Carlo results for β > 1.6. It also makes the mean-field result identical, within a narrow margin, to ressumed strong coupling results in the interval 1.6 < β < 2.4, thus showing the absence of a phase transition.For both groups studied, we find that the asymptotic series of mean-field perturbation theory give much better approximations than do ordinary weak coupling series.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Stochastic perturbative derivation of the axial anomaly

The axial anomaly is calculated as the infinite Langevin time limit of stochastic triangle diagrams. Their regularization is insured with the help of an analytic stochastic regulator. The usual axial anomaly is recovered only when the Langevin equations used to generate the perturbative expansion are gauge covariant.     

On the anti-symmetric vierbein in quantum supergravity

We consider the BRS identities for N = 1 supergravity in a covariant gauge. It is shown that, as in the axial gauge, the anti-symmetric part of the vierbein does contribute to the BRS identities, even though one can choose a gauge in which it does not propagate.     

Lorentz-non-invariant counter-terms in QCD in a general axial gauge

It is shown in the context of a pure Yang-Mills theory that the solution of the Slavnov-Taylor identities in a general axial gauge admits counter-terms which may or may not be Lorentz invariant. It follows from the background field method that these counter-terms must be gauge invariant. The Lorentz-non-invariant counter-terms appear already at the one-loop level and depend both on the gauge parameter α and the non-covariant vector n_ω.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

Admissibility of the axial gauge in QED2

The question recently raised by Tyburski as to whether the axial gauge can be used in two-dimensional quantum electrodynamics is examined. It is shown that even if the arguments leading to A₁≠0 are accepted, the consequences is no more than the existence of an uncoupled massless field in the theory. Thus QED₂ calculations based on the axial gauge do not require reconsideration.     

The fate of the U(1) goldstone boson

In the framework of a manifestly covariant formulation of (non-Abelian) gauge theories, we analyse what the gauge invariance (BRS invariance) implies for the problem of the Goldstone boson associated with the conserved U(1) axial vector current. Based on the symmetry consideration of gauge invariance only, it is shown that the Goldstone boson does not appear as a physical particle at all, if and only if the Faddeev-Popov (FP) ghost forms a massless bound state with the gauge boson in a pseudoscalar channel. This decoupling of the Goldstone boson from the physical sector is not caused by the Goldstone dipole proposed by Kogut and Susskind, but by a Goldstone quartet including the FP ghost bound state. This decoupling mechanism by the Goldstone quartet can be shown to become equivalent to that of the Goldstone dipole, only in a special case, i.e., the Schwinger model which is an Abelian theory in two dimensions. In the Abelian gauge theory in four dimensions, the chiral U(1) Goldstone boson necessarily appears as a physical particle.     

The supersymmetric Adler-Bardeen theorem and regularization by dimensional reduction

We examine the subtraction scheme dependence of the anomaly of the supersymmetric, gauge singlet axial current in pure and coupled supersymmetric Yang-Mills theories. Preserving supersymmetry and gauge invariance explicitly by using supersymmetric background field theory and dimensional reduction, we show that only the one-loop value of the axial anomaly is subtraction scheme independent, and that one can always define a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. In general this subtraction scheme may be non-minimal, but in both the pure and the coupled theories, the Adler-Bardeen theorem is satisfied to two loops in minimal subtraction.     

Numerical calculation of the momentum-space gluon propagator in quenched,reduced QCD3

A recently developed method of momentum-space Monte Carlo is applied to compute the momentum-space gluon propagator in quenched, reduced, continuum QCD₃ in axial gauge. There is some evidence that the gluon propagator D_μν(p) is finite as p → 0, which might indicate the existence of a non-perturbative gluon mass.     

Strong-coupling planar diagrams,random surfaces,and the large-N phase transition in U(N) lattice gauge theories

The strong-coupling expansion of U(N) gauge theory on a D-dimensional lattice is reformulated in the limit N → ∞ through a set of diagrammatic rules directly for the free energy and Wilson loops. The strong-coupling planar diagrams are interpreted as surfaces embedded in the lattice. The large-N phase transition is related to the entropy of these surfaces. It is shown that the strong-coupling phase of the U(∞) gauge theory terminates with a phase transition of Gross-Witten type only in 2 and 3 dimensions. When D⩾4 the large-N singularity takes place in a metastable phase because of an earlier first-order transition to the weak-coupling phase of the theory.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.     

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory are carried out numerically up to order g⁴. Comparison of the results with those of the Monte Carlo calculations shows that there exists a non-perturbative contribution of an essential singularity type which may be identified as the string tension.     

Gauge invariant unified field structures,quantizable dynamical systems,charge, and spin structures

Gauge invariant unified field structures on a manifold B are introduced. Necessary and sufficient conditions for their existence are studied. The connection with charge is studied; it is shown that such gauge invariant structures, e.g. quantizable dynamical systems, over simply connected manifolds B are completely classified by charge. Complex analytic gauge invariant unified field structures are studied. These structures over a complex analytic manifold B whose square is the canonical line bundle are in bijective correspondence with the spin structures on B. Finally, a class of homogeneous quantizable dynamical systems are shown not to carry spin structure.