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arXiv:quant-ph/0306189

Reply to "No spin-statistics connection in nonrelativistic quantum mechanics"

Murray Peshkin

Published Jun 27, 2003• 3 citations
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Abstract

In a previous paper [quant-ph/0207017] I gave an elementary proof, starting from stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles must be bosons. Since then it has been suggested that my proof assumed its conclusion, and that it is based on a theory "quite different from standard physics." [quant-ph/0304088] I show here that those two statements are incorrect.

DOI
10.48550/arxiv.quant-ph/0306189

Related papers

Reply to “Comment on ‘Spin and statistics in nonrelativistic quantum mechanics: The spin-zero case’ ”

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The preceding Comment states that I have assumed the conclusion in my proof from nonrelativistic quantum mechanics that spin-zero particles must be bosons, and that the theory presented is different from standard quantum mechanics. I show here that neither of those statements is true.

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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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No spin-statistics connection in nonrelativistic quantum mechanics

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We emphasize that there is no spin-statistics connection in nonrelativistic quantum mechanics. In several recent papers, including Phys. Rev. A 67, 042102 (2003) [quant-ph/0207017], quantum mechanics is modified so as to force a spin-statistics connection, but the resulting theory is quite different from standard physics.

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Comment on “Spin and statistics in nonrelativistic quantum mechanics: The spin-zero case”

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We emphasize that there is no spin-statistics connection in nonrelativistic quantum mechanics. In several recent papers [including Phys. Rev. A 67, 042102 (2003)], quantum mechanics is modified so as to force a spin-statistics connection, but the resulting theory is quite different from standard physics.

Physical Review A•Oct 14, 2003•13 citations

Spin and statistics in nonrelativistic quantum mechanics: The spin-zero case

Murray Peshkin

It is proved from stated assumptions of nonrelativistic quantum mechanics based on the Schroedinger equation that identical spin-zero particles must obey symmetric statistics.

arXiv:quant-ph/0207017•Physical Review A•Apr 4, 2003•19 citations

On Spin and Statistics in Quantum Mechanics

Peshkin, M

It is proved from the assumptions of nonrelativistic quantum mechanics that identical spin-zero particles must obey symmetric statistics.

•Jul 3, 2002•1 citation
In a previous paper [quant-ph/0207017] I gave an elementary proof, starting from stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles must be bosons. Since then it has been suggested that my proof assumed its conclusion, and that it is based on a theory "quite different from standard physics." [quant-ph/0304088] I show here that those two statements are incorrect.
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.