Covariant spinor representation of $iosp(d,2/2)$ and quantization of the spinning relativistic particle

TL;DR

This paper constructs a covariant spinor representation of the $iosp(d,2/2)$ algebra for quantizing the spinning relativistic particle, linking it to the BFV-BRST quantization and enabling cohomological analysis of physical states.

Contribution

It introduces a novel covariant spinor representation of $iosp(d,2/2)$ and connects it to the canonical BFV-BRST quantization framework for spinning particles.

Findings

Representation matches the state space from BFV-BRST quantization.

Physical states can be determined from the algebra's representation theory.

The approach simplifies cohomological analysis of the model.

Abstract

A covariant spinor representation of $iosp(d,2/2)$ is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the $iosp(d,2/2)$ algebra.