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arXiv:quant-ph/0207017 · Physical Review A

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

Murray Peshkin

Published Apr 4, 2003• 19 citations
arXivHTMLPDF

Abstract

It is proved from stated assumptions of nonrelativistic quantum mechanics based on the Schroedinger equation that identical spin-zero particles must obey symmetric statistics.
DOI
10.1103/physreva.67.042102

Related papers

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

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

Murray Peshkin

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.

Physical Review A•Oct 14, 2003•14 citations

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

Murray Peshkin

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.

arXiv:quant-ph/0306189•Jun 27, 2003•3 citations

Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles

Takafumi Kita

A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a $π$-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.

quant-pharXiv:2512.12071•Dec 16, 2025•0 citations

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

Roland E. Allen, Alfonso Mondragón

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

Quantum Statistics of Identical Particles

J. C. Garrison

Abstract The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group.

arXiv:2207.13231•Foundations of Physics•Jul 14, 2022•1 citation
A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a πππ-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.
Abstract The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group.