The permutation symmetry of Newtonian stationary-state functions – such
as the total momentum and the Hamiltonian – is crucial for correct state counting in
classical statistical mechanics, but plays virtually no role for classical many-body
systems. In contrast, it yields novel effects for quantum many-body systems of
equal/identical particles. In order to avoid the misunderstandings Jaynes (1992) has
rightly stressed, basic notions, such as equal and identical particles, (in)distinguishability
and exchangeability (the really relevant notion) are discussed first within
classical mechanics. Then, they are applied to the weight (limiting) functions. The
permutation symmetry of the wave functions follow largely from that of the weight
functions. The different effects for bosons and fermions are mentioned and illustrated.
For the generalization towards anyons and the fractional quantum Hall effect, some
ideas for further exploration are proposed. Entanglement is treated as a consequence
of the conservation laws, in particular, for the angular momentum.
Keywords: Angular momentum, Bose-Einstein condensation, Boson, Conservation
law, Entanglement, Equal particles, Exchange hole, Exchangeability,
Fermion, Fractional quantum Hall effect, Hamiltonian, Identical particles,
Indistinguishability, Jaynes, Limiting functions, Many-body system, Newtonian
stationary-state function, Pauli ban, Permutation symmetry, Total momentum,
Weight functions.
