Finite Nilpotent BRST transformations in Hamiltonian formulation

TL;DR

This paper extends the finite field dependent BRST transformations to Hamiltonian systems using the Batalin-Fradkin-Vilkovisky method, showing how they relate different theories and resemble canonical transformations.

Contribution

It introduces a Hamiltonian formulation of FFBRST transformations with explicit calculation of Jacobians and demonstrates their connection to effective theories and canonical transformations.

Findings

Jacobian of FFBRST can be expressed as an exponential of a local functional.

FFBRST transformations connect different effective Hamiltonian theories.

FFBRST transformations are similar to canonical transformations in extended phase space.

Abstract

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformtaions in the sector of Lagrange multiplier and its corresponding momenta.