Lagrange Anchor and Characteristic Symmetries of Free Massless Fields

TL;DR

This paper introduces a Poincaré covariant Lagrange anchor for non-Lagrangian equations describing free massless fields of spin greater than 1/2, enabling symmetry assignment and path-integral quantization.

Contribution

It provides a novel covariant Lagrange anchor for non-Lagrangian relativistic wave equations of massless fields, facilitating their quantization.

Findings

Established a covariant Lagrange anchor for spin > 1/2 fields

Linked conservation laws to symmetries via the Lagrange anchor

Enabled path-integral quantization of non-Lagrangian equations

Abstract

A Poincar\'e covariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin $s>1/2$ in four-dimensional Minkowski space. By making use of this Lagrange anchor, we assign a symmetry to each conservation law and perform the path-integral quantization of the theory.