BRST approach to Lagrangian construction for bosonic continuous spin field

TL;DR

This paper develops a BRST-based covariant Lagrangian formulation for bosonic continuous spin fields, simplifying the analysis of their representation and equations in four-dimensional spacetime.

Contribution

It introduces a new formulation of continuous spin representations that reduces the complexity of the equations and derives a covariant Lagrangian using the BRST approach.

Findings

Simplified the analysis of Bargmann-Wigner equations for continuous spin fields.

Reduced the number of equations from four to three.

Derived a covariant Lagrangian for continuous spin fields.

Abstract

We formulate the conditions defining the irreducible continuous spin representation of the four-dimensional Poincar\'e group based on spin-tensor fields with dotted and undotted indices. Such a formulation simplifies analysis of the Bargmann-Wigner equations and reduces the number of equations from four to three. Using this formulation we develop the BRST approach and derive the covariant Lagrangian for the continuous spin fields.