Does the nontrivially deformed field-antifield formalism exist?

TL;DR

This paper explores the existence of a nontrivially deformed field-antifield BV formalism by reformulating it using a generalized Euler vector field, extending the usual power-counting operator in a gauge-invariant way.

Contribution

It introduces a reformulation of the deformed BV formalism using a general Euler vector field, providing a gauge-fixing mechanism within this new framework.

Findings

Reformulation of the deformed BV formalism using a generalized Euler vector field.

Extension of the power-counting operator in an antisymplectic-invariant manner.

Implementation of gauge-fixing in the deformed formalism.

Abstract

We reformulate the Lagrange deformed field-antifield BV -formalism suggested, in terms of the general Euler vector field $N$ generated by the antisymplectic potential. That $N$ generalizes, in a natural anticanonically-invariant manner, the usual power-counting operator. We provide for the "usual" gauge-fixing mechanism as applied to the deformed BV -formalism.