Indistinguishability for quantum particles: Spin, statistics and the geometric phase. (English) Zbl 0892.46084

Berry, M. V.; Robbins, J. M.

Proc. R. Soc. Lond., Ser. A 453, No. 1963, 1771-1790 (1997).

A complete understanding of the relation between spin and statistics in non-relativistic quantum mechanics is still lacking. Berry and Robbins argue that the Pauli sign, i.e. the phase factor \((-1)^{2s}\) accompanying the spin exchange for two identical particles with \(\text{spin }s\), as a geometric phase, is in fact of topological origin, associated with non-contractible loops in the doubly connected configuration space (obtained by identifying antipodes). It is shown that the present theory extends to an arbitrary number of identical particles.

Reviewer: G.Roepstorff (Aachen)

MSC:

46N50	Applications of functional analysis in quantum physics
81P05	General and philosophical questions in quantum theory
81R05	Finite-dimensional groups and algebras motivated by physics and their representations

Keywords:

Pauli principle; geometric phase; spin and statistics; non-relativistic quantum mechanics; Pauli sign