zbMATH — the first resource for mathematics

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

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
Full Text: DOI