Satish D. Joglekar

APPLICATION OF FINITE FIELD-DEPENDENT BRS TRANSFORMATIONS TO PROBLEMS OF THE COULOMB GAUGE

We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge has to be treated as the gauge parameter λ → 0 limit. We further find that the propagator so obtained has good high energy behavior for λ ≠ 0 and ∊ ≠ 0. We also find that the behavior of the propagator so obtained is sensitive to the order of limits k0 → ∞, λ → 0 and ∊ → 0; so that these have to be handled carefully in a higher loop calculation. We show that we can arrive at the result of Cheng and Tsai for the ambiguous two-loop Feynman integrals without the need for an extra ad hoc regularization and within the path integral formulation.

CORRECT TREATMENT OF

The propagators in axial-type, light-cone and planar gauges contain 1/(\eta\cdot k)^p-type singularities. These singularities have generally been treated by inventing prescriptions for them. In this work, we propose an alternative procedure for treating these singularities in the path integral formalism using the known way of treating the singularities in Lorentz gauges. To this end, we use a finite field-dependent BRS transformation that interpolates between Lorentz-type and the axial-type gauges. We arrive at the

\bm{{1\over (\eta\cdot{\lc{k}})^{\lc{p}}}}

\epsilon

SINGULARITIES IN THE AXIAL GAUGE PROPAGATOR

-dependent tree propagator in the axial-type gauges. We examine the singularity structure of the propagator and find that the axial gauge propagator so constructed has {\it no} spurious poles (for real

Finite field-dependent BRS transformation and axial gauges

k

Causality violation in nonlocal quantum field theory

). It however has a complicated structure in a small region near

Relating Green’s functions in axial and Lorentz gauges using finite field-dependent BRS transformations

\eta\cdot k=0

Z' in the 3-3-1 model

. We show how this complicated structure can effectively be replaced by a much simpler propagator.

WILSON LOOP AND THE TREATMENT OF AXIAL GAUGE POLES

Finite field-dependent BRS (FFBRS) transformation is a generalization of ordinary BRS transformation that can be used to connect actions in different gauge. In this work, we develop the FFBRS transformation that connects the usual Lorentz gauges (with gauge parameter ) with axial gauges (with gauge parameter ). We suggest a possible application of this result to rigorously obtain the prescription of the type singularity.

GREEN'S FUNCTIONS IN AXIAL- AND LORENTZ-TYPE GAUGES AND BRS TRANSFORMATIONS

We study the causality violation in the nonlocal ϕ4-theory (as formulated by Kleppe and Woodard) containing a finite mass scale Λ. Starting from the Bogoliubov–Shirkov criterion for causality, we construct and study combinations of S-matrix elements that signal violation of causality in the one-loop approximation. We find that the causality violation in the exclusive process ϕ+ϕ→ϕ+ϕ grows with energy, but the growth with energy, (for low to moderate energies) is suppressed to all orders compared to what one would expect purely from dimensional considerations. We however find that the causality violation in other processes such as ϕ+ϕ→ϕ+ϕ+ϕ+ϕ grows with energy as expected from dimensional considerations at low to moderate energies. For high enough energies comparable to the mass scale Λ, however, we find a rapid (exponential-like) growth in the degree of causality violation. We suggest a scenario, based on an earlier work, that will enable one to evade a large theoretical causality violation at high energies, should it be unobserved experimentally.