Classical and Quantum Gauged Massless Rarita-Schwinger Fields

TL;DR

This paper demonstrates that massless Rarita-Schwinger fields coupled to gauge fields can be consistently formulated at both classical and quantum levels, revealing a generalized fermionic gauge invariance and avoiding superluminal propagation issues.

Contribution

It provides a consistent classical and quantum framework for massless gauged Rarita-Schwinger fields, including gauge invariance and correct propagation properties, which contrasts with the massive case.

Findings

Massless Rarita-Schwinger fields exhibit consistent gauge invariance.

Wave modes do not propagate superluminally.

Quantum theory maintains positivity and covariance properties.

Abstract

We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields consistent classical and quantum theories, with a generalized fermionic gauge invariance. 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. The quantized case is studied in gauge covariant radiation gauge and $\Psi_0=0$ gauge for the Rarita-Schwinger field, by both functional integral and Dirac bracket methods. In $\Psi_0=0$ gauge, the constraints have the form needed to apply the Faddeev-Popov method for deriving a functional integral. The Dirac bracket approach in $\Psi_0=0$ gauge yields consistent Hamilton equations of motion, and in covariant radiation gauge leads to anticommutation relations with the correct positivity properties. We discuss relativistic covariance of the anticommutation relations, and of Rarita-Schwinger scattering from an Abelian potential. We note that fermionic gauge transformations are a canonical transformation, but further details of the transformation between different fermionic gauges are left as an open problem.