Stress and Strain: T^{\mu\nu} of Higher Spin Gauge Fields

TL;DR

This paper analyzes the stress tensors of free higher spin gauge fields, expressing them in gauge-invariant terms, verifying Poincare algebra, and discussing implications for higher spin interactions.

Contribution

It introduces a gauge-invariant formulation of stress tensors for higher spin fields and verifies their algebraic properties, addressing challenges in higher spin interactions.

Findings

Stress tensors can be expressed in gauge-invariant form using nonlocal variables.

Poincare algebra is verified for the constructed generators.

Relevance to interaction difficulties in higher spin systems is discussed.

Abstract

We present some results concerning local currents, particularly the stress tensors T^{\mu\nu}, of free higher (>1) spin gauge fields. While the T^{\mu\nu} are known to be gauge variant, we can express them, at the cost of manifest Lorentz invariance, solely in terms of (spatially nonlocal) gauge-invariant field components, where the "scalar" and "spin" aspects of the systems can be clearly separated. Using the fundamental commutators of these transverse-traceless variables we verify the Poincare algebra among its generators, constructed from the T^0_\mu and their moments. The relevance to the interaction difficulties of higher spin systems is mentioned.