Remarks on Existence of Proper Action for Reducible Gauge Theories

TL;DR

This paper reviews and introduces new proofs for the existence and uniqueness of proper actions in reducible gauge theories within the field-antifield formalism, ensuring their implementation at quadratic order.

Contribution

It provides two novel existence proofs using new resolution degrees, expanding the understanding of proper actions in reducible gauge theories.

Findings

Existence of proper actions for reducible gauge theories confirmed.

New proof methods based on reduced and shifted antifield numbers introduced.

Proper actions can implement gauge generators at quadratic order.

Abstract

In the field-antifield formalism, we review existence and uniqueness proofs for the proper action in the reducible case. We give two new existence proofs based on two resolution degrees called "reduced antifield number" and "shifted antifield number", respectively. In particular, we show that for every choice of gauge generators and their higher stage counterparts, there exists a proper action that implements them at the quadratic order in the auxiliary variables.