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Indistinguishability for Quantum Particles: Further Considerations
Berry, M.V.; Robbins, J.M.
Keyword(s): spin-statistics relation; pauli exclusion principle
Abstract: Our earlier arguments (Berry, M.V. & Robbins, J.M. 1997. Proc Roy. Soc. Lond. A453 1771-1790) leading to the spin-statistics relation are summarized and then revisited. Correcting a minor logical error in the double application of exchange reinforces the parallel transport requirement for the basis incorporating spin exchange. There are certain 'perverse' constructions, satisfying all our previous requirements but leading to the wrong exchange sign (e.g. replacing commutators by anticommutators in the Schwinger representation of the spins of the particles); we suggest why these are unacceptable. In our previous arguments, no use was made of relativity; we comment on this, and on the fact that spin is equally a consequence of galilean as of einsteinian relativity. Finally, we obtain an extended spin-statistics relation for identical particles that possess properties additional to position and spin.
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