Generalized Symmetries of Massless Free Fields on Minkowski Space

TL;DR

This paper classifies all local symmetries of massless free fields in Minkowski space, revealing conformal, dual, and chiral symmetries, including higher-order extensions, for various fundamental equations.

Contribution

It provides a complete explicit classification of generalized symmetries for massless free fields of spin s ≥ 1/2, including new chiral and higher-order symmetries.

Findings

Classified symmetries of Dirac-Weyl neutrino, Maxwell, and linearized gravity equations.

Identified conformal, dual, and chiral symmetries and their higher-order extensions.

Established a comprehensive framework for symmetries of massless free fields.

Abstract

A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin $s \geq 1/2$ is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral symmetries of order $2s$, and their higher-order extensions obtained by Lie differentiation with respect to conformal Killing vectors. In particular, the results yield a complete classification of generalized symmetries of the Dirac-Weyl neutrino equation, Maxwell's equations, and the linearized gravity equations.