On general Lagrangian formulations for arbitrary mixed-symmetric higher-spin fermionic fields on Minkowski backgrounds

TL;DR

This paper develops a comprehensive Lagrangian formulation for arbitrary mixed-symmetric higher-spin fermionic fields in Minkowski space, extending previous bosonic work and utilizing advanced algebraic and BRST methods to describe both massless and massive fields.

Contribution

It introduces a universal approach to construct gauge-invariant Lagrangians for mixed-symmetric higher-spin fermionic fields using Verma modules, oscillator realizations, and BRST-BFV methods.

Findings

Unified Lagrangian formulations for arbitrary mixed-symmetric fermionic fields.

Explicit construction of gauge-invariant actions with reducible gauge symmetries.

Applicability to both massless and massive higher-spin fermionic fields.

Abstract

The details of unconstrained Lagrangian formulations (being continuation of earlier developed research for Bose particles in NPB 862 (2012) 270, [arXiv:1110.5044[hep-th]], Phys. of Part. and Nucl. 43 (2012) 689, [arXiv:1202.4710 [hep-th]]) are reviewed for Fermi particles propagated on an arbitrary dimensional Minkowski space-time and described by the unitary irreducible half-integer higher-spin representations of the Poincare group subject to Young tableaux $Y(s_1,...,s_k)$ with $k$ rows. The procedure is based on the construction of the Verma modules and finding auxiliary oscillator realizations for the orthosymplectic $osp(1|2k)$ superalgebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Applying of an universal BRST-BFV approach permit to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive fermionic fields of any spin with appropriate number of gauge and Stukelberg fields. The general construction possesses by the obvious possibility to derive Lagrangians with only holonomic constraints.