2003/01/07 by Steven French, S. R. D. French, French, S. R. D. +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Advanced Graph Theory Research #FOS: Physical sciences #Quantum Physics (quant-ph) #graph theory and CDMA systems #quant-ph #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.quant-ph/0301020
To appear in "Symmetries in physics: philosophical reflections", edited by Katherine Brading and Elena Castellani, Cambridge University Press, 2003
arxiv created 2003/01/07 · openalex publication_date 2003/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
\noindent In our contribution to this volume we deal with discrete symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In physics we find that discrete symmetries frequently arise as `internal', non-spacetime symmetries. Permutation symmetry is such a discrete symmetry arising as the mathematical basis underlying the statistical behaviour of ensembles of certain types of indistinguishable quantum particle (e.g., fermions and bosons). Roughly speaking, if such an ensemble is invariant under a permutation of its constituent particles (i.e., permutation symmetric) then one doesn't `count' those permutations which merely `exchange' indistinguishable particles; rather, the exchanged state is identified with the original state. This principle of invariance is generally called the `indistinguishability postulate' [IP], but we prefer to use the term `permutation invariance' [PI]. It is this symmetry principle that is typically taken to underpin and explain the nature of (fermionic and bosonic) quantum statistics (although, as we shall see, this characterisation is not uncontentious), and it is this principle that has important consequences regarding the metaphysics of identity and individuality for particles exhibiting such statistical behaviour.