Quantization of pseudoclassical model of spin one relativistic particle

TL;DR

This paper develops a canonical quantization method for a pseudoclassical spin one relativistic particle, demonstrating equivalence to Proca and Maxwell theories in massive and massless cases respectively, and compares it with spin one-half particles.

Contribution

It introduces a consistent quantization procedure for the pseudoclassical model of spin one particles, including approaches for massless and massive cases, and establishes their equivalence to known field theories.

Findings

Quantization for massive case is equivalent to Proca theory.

Quantization for massless case is equivalent to Maxwell theory.

Comparison with spin one-half particles highlights differences and similarities.

Abstract

A consistent procedure of canonical quantization of pseudoclassical model for spin one relativistic particle is considered. Two approaches to treat the quantization for the massless case are discussed, the limit of the massive case and independent quantization of a modified action. Quantum mechanics constructed for the massive case proves to be equivalent to the Proca theory and for massless case to the Maxwell theory. Results obtained are compared with ones for the case of spinning (spin one half) particle.