On the Geometry of the Berry-Robbins Approach to Spin-Statistics

TL;DR

This paper explores the geometric structures underlying the spin-statistics connection, comparing them with the Berry-Robbins approach, and introduces a global geometric method for quantum indistinguishability that supports this approach.

Contribution

It provides a geometric and algebraic framework that enhances understanding of the spin-statistics relation and offers a model-independent way to treat wave function singlevaluedness.

Findings

Supports the Berry-Robbins approach with geometric structures

Introduces a global geometric method for quantum indistinguishability

Provides a model-independent perspective on wave function singlevaluedness

Abstract

Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support for this approach. In our work, a geometric approach to quantum indistinguishability is introduced which allows the treatment of singlevaluedness of wave functions in a global, model independent way.