BFV-Type Representation of Path-Integral for Dynamical System with second class constraints

TL;DR

This paper extends the phase space of constrained dynamical systems with ghost variables, constructs a BFV-type path integral representation, and demonstrates its equivalence to the standard formulation.

Contribution

It introduces a BFV-type path integral framework for systems with second class constraints, linking it to existing formalisms.

Findings

BFV-type path integral matches the standard representation

Ghost variables enable extension of phase space for second class constraints

Formal analogies of $ mbda$-charge and Hamiltonian are established

Abstract

It is shown that the phase space of a dynamical system subject to second class constraints can be extended by ghost variables in such a way that some formal analogies of the $\Omega$-charge and the unitarizing Hamiltonian can be constructed. Then BFV-type path integral representation for the generating functional of Green's functions is written and shown to coincide with the standard one.