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Reply to "Non-relativistic proofs of the spin-statistics connection," by Shaji and Sudarshan

Murray Peshkin
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Abstract

I earlier proved under stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles with no internal degrees of freedom must be bosons. Shaji and Sudarshan have criticized that proof, asserting that it is "based on single-valuedness under rotation of the wave functions of systems of identical particles." No such assumption was used. Here, to remove all doubt, I exclude the fermion possibility through a proof in which even the existence of rotation is not used. Following that, I assume that the Hilbert space is invariant under rotation to exclude other symmetries which correspond neither to bosons nor to fermions. In that proof no issue of single-valuedness can arise.

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Murray Peshkin. 2004-02-17. Reply to "Non-relativistic proofs of the spin-statistics connection," by Shaji and Sudarshan. https://arxiv.org/abs/quant-ph/0402118

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