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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.

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
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