Hamiltonian and Lagrangian BRST quantization in Riemann Manifold

TL;DR

This paper develops a comprehensive BRST quantization framework for particle motion on a hypersurface in Euclidean space, utilizing Hamiltonian and Lagrangian formalisms, and applying BFFT, BFV, and Batalin-Vilkovisky formalisms.

Contribution

It introduces a unified approach to BRST quantization on constrained manifolds using BFFT and BFV formalisms, including a detailed example and discussion of Batalin-Vilkovisky formalism.

Findings

Successfully converts second class constraints into first class constraints.

Constructs BRST symmetry using BFV analysis.

Provides a detailed example illustrating the formalism.

Abstract

The BRST quantization of particle motion on the hypersurface $V_{(N-1)}$ embedded in Euclidean space $R_N$ is carried out both in Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) formalism, the second class constrained obtained using Hamiltonian analysis are converted into first class constraints. Then using BFV analysis the BRST symmetry is constructed. We have given a simple example of these kind of system. In the end we have discussed Batalin-Vilkovisky formalism in the context of this (BFFT modified) system.