A Note on Abelian Conversion of Constraints

TL;DR

This paper demonstrates a closed-form Abelian conversion for systems with linear second class constraints and explores the resulting shift symmetry in the context of BV quantization.

Contribution

It provides a new explicit method for Abelian conversion of linear second class constraints and links it to shift symmetries in BV quantization.

Findings

Closed-form Abelian conversion for linear second class constraints

First class constraints generate a generalized shift symmetry

Application to first order Lagrangian systems

Abstract

We show that for a system containing a set of general second class constraints which are linear in the phase space variables, the Abelian conversion can be obtained in a closed form and that the first class constraints generate a generalized shift symmetry. We study in detail the example of a general first order Lagrangian and show how the shift symmetry noted in the context of BV quantization arises.