Covariant scalar representation of $iosp(d,2/2)$ quantization of the scalar relativistic particle

TL;DR

This paper develops a covariant scalar representation of the $iosp(d,2/2)$ algebra for quantizing the scalar relativistic particle, linking it to the BFV-BRST method and enabling physical state determination through algebraic representation theory.

Contribution

It introduces a new covariant scalar representation of $iosp(d,2/2)$ and connects it with established quantization methods for the scalar relativistic particle.

Findings

Representation aligns with BFV-BRST quantization results.

Physical states can be derived from algebraic cohomology.

Provides a new algebraic approach to particle quantization.

Abstract

A covariant scalar representation of $iosp(d,2/2)$ is constructed and analysed in comparison with existing methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this $iosp(d,2/2)$ produced representation can be identified with the state space arising from the canonical BFV-BRST quantization of the modular invariant, unoriented scalar particle (or antiparticle) with admissible gauge fixing conditions. 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.