Adjustment of Faddeev-Popov quantization to reducible gauge theories: antisymmetric tensor fermion in $AdS_d$ space

TL;DR

This paper develops a method to adjust Faddeev-Popov quantization for reducible gauge theories, applied to antisymmetric tensor fermions in AdS space, resulting in a more efficient ghost structure and effective action derivation.

Contribution

The paper introduces a nested factorization method for quantizing reducible gauge theories, reducing ghost count and aligning with BV formalism for first-stage reducibility.

Findings

Method yields fewer ghosts than traditional approaches.

Successfully quantized antisymmetric tensor fermion in AdS space.

Derived effective action using functional determinants.

Abstract

We develop the method adjusting the Faddeev-Popov factorization procedure for the quantization of generic reducible gauge theories with linearly dependent generators and apply it to the first stage reducible model of second rank antisymmetric fermion in d-dimensional AdS spacetime. The method consists in nested factorizations of the gauge group volume for the determination of the consistently defined delta function of reduced gauge conditions, group integration measure and gauge-fixed contribution of ghosts. It is compared to the Batalin-Vilkovisky (BV) formalism of quantizing theories with linearly dependent generators and shown to be equivalent to it for first stage reducible theories. Nevertheless, the method under consideration, unlike the BV formalism, from the very beginning leads to the functional integral with fewer number of ghosts. Using this method we quantized the variant of fermionic totally antisymmetric tensor-spinor theory in AdS space and derived its effective action in terms of the functional determinants of special Dirac-type operators. Limitations of the method are also discussed along with the prospects of its extension to higher reducibility stages and higher rank models of antisymmetric fermions.