On the mixed symmetry irreducible representations of the Poincare group in the BRST approach

TL;DR

This paper develops a BRST-based method to describe irreducible massless Poincare group representations with mixed symmetry, providing explicit examples like the notoph and Weyl tensor.

Contribution

It introduces a novel BRST approach for mixed symmetry representations of the Poincare group, including auxiliary algebraic constructions and explicit examples.

Findings

Explicit Lagrangian descriptions for mixed symmetry massless fields

Construction of auxiliary representations using Verma modules

Application to examples like the notoph and Weyl tensor

Abstract

The lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose is used the method of the BRST constructions adopted to the systems of second class constraints by the construction of an auxiliary representations of the algebras of constraints in terms of Verma modules.