Finite field dependent BRST transformations and its applications to gauge field theories

TL;DR

This paper extends finite field dependent BRST transformations and explores their applications in gauge theories, addressing issues like Gribov ambiguity and constrained dynamics, with new symmetries and quantization methods.

Contribution

It introduces on-shell and off-shell FF-anti-BRST transformations, a new combined symmetry, and applies BFV quantization and differential geometry concepts to gauge theories.

Findings

Extended FFBRST in auxiliary field formulation.

Developed on-shell and off-shell FF-anti-BRST transformations.

Applied transformations to Gribov problem and constrained dynamics.

Abstract

The Becchi-Rouet-Stora and Tyutin (BRST) transformation plays a crucial role in the quantization of gauge theories. The BRST transformation is also very important tool in characterizing the various renormalizable field theoretic models. The generalization of the usual BRST transformation, by making the infinitesimal global parameter finite and field dependent, is commonly known as the finite field dependent BRST (FFBRST) transformation. In this thesis, we have extended the FFBRST transformation in an auxiliary field formulation and have developed both on-shell and off-shell FF-anti-BRST transformations. The different aspects of such transformation are studied in Batalin-Vilkovisky (BV) formulation. FFBRST transformation has further been used to study the celebrated Gribov problem and to analyze the constrained dynamics in gauge theories. A new finite field dependent symmetry (combination of FFBRST and FF-anti-BRST) transformation has been invented. The FFBRST transformation is shown useful in connection of first-class constrained theory to that of second-class also. Further, we have applied the Batalin-Fradkin-Vilkovisky (BFV) technique to quantize a field theoretic model in the Hamiltonian framework. The Hodge de Rham theorem for differential geometry has also been studied in such context.