Generalized Spin-Statistics Theorem

TL;DR

This paper extends the spin-statistics theorem to both relativistic and non-relativistic quantum theories, using advanced group representation methods and considering internal symmetries and non-relativistic limits.

Contribution

It provides a comprehensive derivation of the spin-statistics theorem in first-quantized form, incorporating internal symmetries and non-relativistic limits, expanding previous proofs.

Findings

Derived the spin-statistics relation for relativistic and non-relativistic cases

Included internal symmetry groups in the derivation

Discussed the consistency of non-relativistic limits

Abstract

We derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter being the universal covering of the Lorentz group. We define the identity of particles. We include theories that have an internal symmetry group. We discuss consistency of the non-relativistic limit.