Massless fields in plane wave geometry

TL;DR

This paper explores the conformal symmetries of plane wave geometries, defining masslessness for higher spin fields, and constructs gauge-invariant equations of motion, revealing their algebraic and representation-theoretic structures.

Contribution

It introduces a conformally invariant definition of masslessness in plane wave geometries and develops gauge-invariant equations for all massless spin fields in this setting.

Findings

Conformal isometry algebras of plane wave geometries are characterized.

Gauge invariant equations for massless higher spin fields are constructed.

Connections between these fields and $u(2,2)$ ladder representations are established.

Abstract

Conformal isometry algebras of plane wave geometry are studied. Then, based on the requirement of conformal invariance, a definition of masslessness is introduced and gauge invariant equations of motion, subsidiary conditions, and corresponding gauge transformations for all plane wave geometry massless spin fields are constructed. Light cone representation for elements of conformal algebra acting as differential operators on wavefunctions of massless higher spin fields is also evaluated. Interrelation of plane wave geometry massless higher spin fields with ladder representation of $u(2,2)$ algebra is investigated.