Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Understanding Permutation Symmetry   \noindent In our contribution to this volume we deal with \emph{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.

10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
2
The categories of this paper are: math
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con