A note on the path integral for systems with primary and secondary second class constraints

TL;DR

This paper demonstrates that the phase space path integral for systems with various second class constraints can be reformulated as a configuration space path integral with a local measure, simplifying the analysis of such constrained systems.

Contribution

It introduces a method to rewrite the phase space path integral for systems with arbitrary second class constraints as a configuration space integral with a local measure.

Findings

Reformulation of phase space path integral as configuration space integral

Applicable to systems with primary and secondary second class constraints

Simplifies the analysis of constrained systems

Abstract

It is shown that the phase space path integral for a system with arbitrary second class constraints (primary, secondary ...) can be rewritten as a configuration space path integral of the exponent of the Lagrangian action with some local measure.