Relativistic Spin-Statistics Connection and Kaluza-Klein Space-Time

TL;DR

This paper generalizes the spin-statistics connection to relativistic and Kaluza-Klein space-times, incorporating internal quantum numbers alongside spin through a unified formalism.

Contribution

It extends the Berry-Robbins formalism to relativistic and higher-dimensional Kaluza-Klein frameworks, integrating internal quantum numbers into the spin-statistics relation.

Findings

Unified relativistic spin-statistics formalism

Inclusion of internal quantum numbers in the connection

Extension to arbitrary Kaluza-Klein space-times

Abstract

The non-relativistic formalism introduced by Berry and Robbins that naturally incorporates the spin-statistics connection is generalized relativistically. It is then extended to an arbitrary Kaluza-Klein space-time by a suitable generalization of the Schwinger treatment of angular momenta. This leads, in this approach, to the inclusion of the `internal' quantum numbers in the spin-statistics connection on an equal footing with spin.