Application of Finite Field-Dependent BRS Transformations to Problems of the Coulomb Gauge

Abstract

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[Formula: see text] 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.

Non-perturbative to perturbative QCD via the FFBRST

“…Group index a is summed over. This FFBRST transformation is particularly different among others [15][16][17][18][19][20][21][22][23][24][25][26][27][28] due to the unique form of transformations (11) and by the fact that the field dependent parameter in Eq. (18) (18), under which the measure changes…”

“…They are thus capable of connecting generating functionals of two different BRST invariant theories and have been used to study different gauge field theoretic models with various effective actions [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In this paper we construct an appropriate FFBRST transformation to establish the connection at the level of generating functionals between the recently introduced quadratic gauge with substantial implications in the non-perturbative QCD [7][8][9] and the familiar Lorenz gauge which is suitable to describe the perturbative QCD.…”

Nilpotent symmetries in supergroup field cosmology

“…The FFBRST transformations have found many important applications in the second quantized gauge field theories [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Therefore, it is worthwhile to study the FFBRST formulation in the case of third quantized super-group field cosmology.…”

Finite field-dependent BRST symmetry for ABJM theory inN=1superspace

“…Even though these finite transformations are a symmetry of the quantum action, they are not a symmetry of the functional measure. They can thus be used to relate a theory in one gauge to the same theory in a different gauge [19][20][21][22][23][24][25][26][27][28]. So, FFBRST transformations can be used to overcome a problem that a theory suffers from in a particular gauge.…”