Quantized Gauged Massless Rarita-Schwinger Fields

TL;DR

This paper investigates the quantization of massless Rarita-Schwinger fields coupled to gauge fields, demonstrating a consistent, Lorentz-invariant approach with positive semidefinite anticommutators using Dirac brackets and functional integrals.

Contribution

It introduces a novel quantization method for gauged massless Rarita-Schwinger fields that ensures Lorentz invariance and positive definiteness, addressing previous inconsistencies.

Findings

Anticommutator has a non-singular limit as gauge fields approach zero

Method yields a Lorentz-invariant, positive semidefinite anticommutator

Functional integral derived using Faddeev-Popov method with consistent constraints

Abstract

We study quantization of a minimally gauged massless Rarita-Schwinger field, by both Dirac bracket and functional integral methods. The Dirac bracket approach in covariant radiation gauge leads to an anticommutator that has a non-singular limit as gauge fields approach zero, is manifestly positive semidefinite, and is Lorentz invariant. The constraints also have the form needed to apply the Faddeev-Popov method for deriving a functional integral, using the same constrained Hamiltonian and inverse constraint matrix that appear in the Dirac bracket approach.