Generalized Einstein Operator Generating Functions

TL;DR

This paper introduces gauge invariant Einstein operators for mixed symmetry higher spin theories, providing explicit action principles and a calculus for operator expressions, advancing the theoretical framework of higher spin gauge fields.

Contribution

It develops a unified method to construct Einstein operators for various mixed symmetry higher spin fields, including explicit actions and equations of motion.

Findings

Provides explicit gauge invariant Einstein operators for mixed symmetry higher spins

Derives action principles for these theories in minimal covariant form

Recovers known equations of motion for specific cases like Labastida's

Abstract

We present gauge invariant, self adjoint Einstein operators for mixed symmetry higher spin theories. The result applies to multi-forms, multi-symmetric forms and mixed antisymmetric and symmetric multi-forms. It also yields explicit action principles for these theories in terms of their minimal covariant field content. For known cases, these actions imply the mixed symmetry equations of motion of Labastida. The result is based on a calculus for handling normal ordered operator expressions built from quantum generators of the underlying constraint algebras.