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Adjustment of Faddeev-Popov quantization to reducible gauge theories: Antisymmetric tensor fermion in AdSd space

Andrei Barvinsky1,*, Ioseph Buchbinder2,†, Vladimir Krykhtin3,‡, and Dmitry Nesterov1,§

  • *Contact author: barvin@td.lpi.ru
  • †Contact author: buchbinder@theor.jinr.ru
  • ‡Contact author: krykhin@tspu.ru
  • §Contact author: nesterov@lpi.ru
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Phys. Rev. D 112, 065021 – Published 25 September, 2025

DOI: https://doi.org/10.1103/mztf-9xzm

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 anti–de Sitter (AdS) spacetime. The method consists of 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.

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Phys. Rev. D 112, 065021– Published 25 September, 2025
  • Received 20 July 2025
  • Accepted 14 August 2025
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