Faddeev-Jackiw Hamiltonian Reduction for Free and Gauged Rarita-Schwinger Theories

TL;DR

This paper applies the Faddeev-Jackiw symplectic Hamiltonian reduction to free and gauged Rarita-Schwinger theories, deriving fundamental brackets suitable for quantization and analyzing their structural properties.

Contribution

It provides a systematic Hamiltonian reduction for Rarita-Schwinger theories, revealing the independence of brackets from mass and gauge fields, and highlights differences in covariant formulations.

Findings

Derived fundamental brackets for Rarita-Schwinger theories

Brackets are independent of mass and gauge fields

Identified non-covariant nature of massless Dirac equations

Abstract

We study the Faddeev-Jackiw symplectic Hamiltonian reduction for 3+1-dimensional free and Abelian gauged Rarita-Schwinger theories that comprise Grassmannian fermionic fields. We obtain the relevant fundamental brackets and find that they are in convenient forms for quantization. The brackets are independent of whether the theories contain mass or gauge fields, and the structure of constraints and symplectic potentials largely determine characteristic behaviors of the theories. We also note that, in contrast to the free massive theory, the Dirac field equations for free massless Rarita-Schwinger theory cannot be obtained in a covariant way.