Massless Rarita-Schwinger equations: Half and three halves spin solution

TL;DR

This paper revisits the degrees of freedom in the massless Rarita-Schwinger theory, clarifying the spin content and challenging the necessity of residual gauge symmetry, supported by explicit solutions and Hamiltonian analysis.

Contribution

It provides a clear identification of the gauge invariant spin components using Behrends-Fronsdal projectors and questions the role of residual gauge symmetry in the massless Rarita-Schwinger theory.

Findings

The gauge invariant part includes spins 1/2 and 3/2.

Explicit solutions support the absence of residual gauge symmetry.

Hamiltonian analysis shows the system is deterministic without additional constraints.

Abstract

Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -- free of arbitrary functions of time -- we argue that the often-invoked residual gauge symmetry lacks fundamental grounding and should not be used to enforce new external constraints. The result is verified by the total Hamiltonian dynamics. We conclude that eliminating the spin-12 mode \textit{via} the extended Hamiltonian dynamics would be acceptable if the Dirac conjecture was assumed; however, this framework does not accurately describe the original Lagrangian system.