On the geometry of quantum indistinguishability

Abstract

An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent geometric properties of such systems in algebraic terms. As an application, the problem of quantum indistinguishability is reformulated in the light of the proposed approach. Previous attempts aiming at a proof of the spin-statistics theorem in non-relativistic quantum mechanics are explicitly recast in the global language inherent to the presented techniques. This leads to a critical discussion of single-valuedness of wave functions for systems of indistinguishable particles. Potential applications of the methods presented in this paper to problems related to quantization, geometric phases and phase transitions in spin systems are proposed.

24 pages

References in corpus (5)

• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• The Spin-Statistics Theorem in Arbitrary Dimensions
• Berry Phases, Quantum Phase Transitions and Chern Numbers
• Remarks on the Configuration Space Approach to Spin-Statistics
• On the Geometry of the Berry-Robbins Approach to Spin-Statistics