Classical Gauged Massless Rarita-Schwinger Fields

TL;DR

This paper demonstrates that massless Rarita-Schwinger fields can be consistently gauged in classical theory, with proper gauge invariance and no superluminal propagation, challenging previous no-go theorems.

Contribution

It provides a detailed classical formulation of gauged massless Rarita-Schwinger fields, including gauge invariance, constraints, and scattering analysis, showing consistency where prior results suggested impossibility.

Findings

Massless Rarita-Schwinger fields are gauge-invariant and consistent in classical theory.

Wave modes do not propagate superluminally.

Adiabatic decoupling fails at zero gauge field, invalidating some no-go theorems.

Abstract

We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields a consistent classical theory, with a generalized fermionic gauge invariance realized as a canonical transformation. To simplify the algebra, we study a two-component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wave-like modes do not propagate with superluminal velocities. An analysis of Rarita-Schwinger spinor scattering from gauge fields shows that adiabatic decoupling fails in the limit of zero gauge field amplitude, invalidating various "no-go" theorems based on "on-shell" methods that claim to show the impossibility of gauging Rarita-Schwinger fields. Quantization of Rarita-Schwinger fields, using many formulas from this paper, is taken up in the following paper.