Vladimir Krykhtin

We develop the quantization of a recently proposed model describing a totally antisymmetric rank- p tensor-spinor field (a fermionic p -form theory) in d -dimensional anti–de Sitter (AdS) space. The model provides a new nontrivial example of a reducible gauge theory, in which gauge transformations are linearly dependent and the degree of reducibility increases with p . It is well-known that in such cases the standard Faddeev-Popov-DeWitt prescription for the generating functional is not applicable. We quantize the fermionic p -form theory using the general Batalin-Vilkovisky formalism, employing two distinct gauge fermions associated with gauge-fixing functions of different admissible ranks, confirming the independence from the gauge choice. As a result, we obtain the quantum effective action in terms of a sequence of functional determinants corresponding to specific Dirac-like operators on AdS space.

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.

We give a brief overview of the BRST approach to the gauge-invariant Lagrangian formulation for free massive higher-spin bosonic fields, focusing on two specific aspects. First, the theory is considered in four-dimensional flat space in terms of spin-tensor fields with two-component undotted and dotted indices. This leads to a significant simplification of the whole approach in comparison with the one where the fields with vector indices were used, since now there is no need to introduce a constraint responsible for the traces of the fields into the BRST charge. Second, we develop an extremely simple and clear procedure to eliminate all the auxiliary fields and prove that the BRST equations of motion identically reproduce the basic conditions for irreducible representations of the Poincáre group with a given mass and spin. Similar to the massless theory, the final Lagrangian for massive higher-spin fields is formulated in triplet form. The BRST formulation leads to a system of fields that are clearly subdivided into the basic spin s field, Zinoviev-like auxiliary fields, Singh–Hagen-like auxiliary fields, and special BRST auxiliary fields. The auxiliary fields can be partially eliminated by gauge fixing and/or using the equations of motion. This allows one to obtain formally different (with different numbers of auxiliary fields) but equivalent Lagrangian formulations.