Rarita-Schwinger Quantum Free Field Via Deformation Quantization

TL;DR

This paper reexamines the Rarita-Schwinger quantum free field using deformation quantization, showing that subsidiary conditions do not alter the formalism compared to the Dirac field, and calculates the propagator.

Contribution

It demonstrates that subsidiary conditions in the Rarita-Schwinger field do not affect deformation quantization, providing new insights into its operator and wave function structure.

Findings

Subsidiary condition does not change the Wigner function

The vector structure constrains wave functions but not operators

RS propagator was successfully calculated

Abstract

Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the deformation quantization formalism, in relation to the Dirac field case. This happens because the vector structure of the RS field imposes constraints on the space of wave function solutions and not on the operator structure. The RS propagator was also calculated within this formalism.