On a quantization of deformed reducible gauge theories

TL;DR

This paper develops a method to quantize deformed reducible gauge theories, converting broken gauge symmetry into an exact gauge-invariant form suitable for covariant quantization, and applies it to massive fermionic tensor fields in AdS space.

Contribution

It introduces a quantization approach for deformed reducible gauge theories using Stueckelberg procedures and applies it to fermionic tensor models in AdS space.

Findings

Successfully converts broken gauge theories into gauge-invariant form

Derives the partition function with all ghost fields included

Calculates one-loop effective actions as functional determinants of Dirac operators

Abstract

We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be converted into exactly gauge-invariant theory which under a suitable choice of gauge conditions can be treated within the formalism of minimal wave operators manageable by the covariant Schwinger-DeWitt technique. We carry out quantization of such a theory in general terms when the initial generators of gauge transformations are of the first and second stages of reducibility and derive its partition function in terms of the functional integral with all corresponding ghost fields. This method is applied to quantization of massive fermionic totally antisymmetric tensor field models in $AdS$ space. One-loop quantum effective action for these models is derived in the form of the functional determinants of special Dirac-type differential operators in various dimensions.