## 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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