On the Multilevel Field--Antifield Formalism with the Most General Lagrangian Hypergauges

TL;DR

This paper extends the multilevel field-antifield formalism to the most general Lagrangian hypergauges, allowing for a covariant construction without unimodularity constraints, and incorporates measure factors into the scheme.

Contribution

It introduces a geometrically covariant multilevel formalism that handles the most general hypergauge functions without unimodularity restrictions.

Findings

Extended formalism to cover general Lagrangian hypergauges.

Incorporated measure factors into the multilevel scheme.

Modified boundary conditions for the quantum master equation.

Abstract

The multilevel field-antifield formalism is constructed in a geometrically covariant way without imposing the unimodularity conditions on the hypergauge functions. Thus the previously given version [1,2] is extended to cover the most general case of Lagrangian surface bases. It is shown that the extra measure factors, required to enter the gauge-independent functional integrals, can be included naturally into the multilevel scheme by modifying the boundary conditions to the quantum master equation.