Continuous spin fields of mixed-symmetry type

TL;DR

This paper develops a new equation-based description for continuous spin massless fields of mixed-symmetry type in Minkowski space, unifying various formulations and clarifying the role of gauge symmetries.

Contribution

It introduces a modified constrained system for describing continuous spin fields, reproduces known formulations, and clarifies the class of allowed field configurations and gauge properties.

Findings

Reproduces Bekaert-Mourad and Schuster-Toro formulations for scalar continuous spin fields.

Identifies the correct class of field configurations to avoid an empty system.

Shows that gauge symmetries are Stueckelberg-like, indicating no genuine gauge invariance.

Abstract

We propose a description of continuous spin massless fields of mixed-symmetry type in Minkowski space at the level of equations of motion. It is based on the appropriately modified version of the constrained system originally used to describe massless bosonic fields of mixed-symmetry type. The description is shown to produce generalized versions of triplet, metric-like, and light-cone formulations. In particular, for scalar continuous spin fields we reproduce the Bekaert-Mourad formulation and the Schuster-Toro formulation. Because a continuous spin system inevitably involves infinite number of fields, specification of the allowed class of field configurations becomes a part of its definition. We show that the naive choice leads to an empty system and propose a suitable class resulting in the correct degrees of freedom. We also demonstrate that the gauge symmetries present in the formulation are all Stueckelberg-like so that the continuous spin system is not a genuine gauge theory.