BRST Theory for Continuous Spin

TL;DR

This paper develops a BRST formulation for continuous spin representations, offering insights into higher spin field theories and their underlying principles, potentially unifying constrained and unconstrained approaches.

Contribution

It introduces a four-constraint BRST framework for continuous spin fields, connecting them to unconstrained higher spin theories and providing a possible physical basis for trace constraints.

Findings

BRST formulation for continuous spin representations derived

Connection established between continuous spin and unconstrained higher spin theories

Hints at a physical rationale for trace constraints in higher spin fields

Abstract

Some puzzling aspects of higher spin field theory in Minkowski space-time, such as the tracelessness constraints and the search for an underlying physical principle, are discussed. A connecting idea might be provided by the recently much researched continuous spin representations of the Poincar\'e group. The Wigner equations, treated as first class constraints, yields to a four-constraint BRST formulation. The resulting field theory, generalizing free higher spin field theory, is one among a set of higher spin theories that can be related to previous work on unconstrained formulations. In particular, it is conjectured that the unconstrained higher spin theory of Francia and Sagnotti is a limit of a continuous spin theory. Furthermore, a simple analysis of the constraint structure reveals a hint of a physical rationale behind the trace constraints.