What price the spin-statistics theorem? |
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Authors: | E C G Sudarshan I M Duck |
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Institution: | (1) Department of Physics, Center for Particle Theory, University of Texas, 78731 Austin, TX, USA;(2) Physics Department, T.W. Bonner Laboratory, Rice University, 77251 Houston, Texas, USA |
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Abstract: | We examine a number of recent proofs of the spin-statistics theorem. All, of course, get the target result of Bose-Einstein
statistics for identical integral spin particles and Fermi-Dirac statistics for identical half-integral spin particles. It
is pointed out that these proofs, distinguished by their purported simple and intuitive kinematic character, require assumptions
that are outside the realm of standard quantum mechanics. We construct a counterexample to these non-dynamical kinematic ‘proofs’
to emphasize the necessity of a dynamical proof as distinct from a kinematic proof. Sudarshan’s simple non-relativistic dynamical
proof is briefly described. Finally, we make clear the price paid for any kinematic ‘proof’. |
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Keywords: | Spin-statistics rotational invariance non-relativistic fields |
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