Remarks on the Configuration Space Approach to Spin-Statistics

TL;DR

This paper constructs angular momentum operators for indistinguishable particles using a rigorous mathematical approach, offering insights into spin-statistics and potential alternative proofs of the theorem.

Contribution

It introduces a mathematically rigorous method to define angular momentum operators for arbitrary spins in indistinguishable particle systems, connecting to existing approaches.

Findings

Constructed angular momentum operators for two spin-zero particles.

Discussed the connection with other configuration space approaches.

Explored implications for alternative proofs of the spin-statistics theorem.

Abstract

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.