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

• URL: http://arxiv.org/abs/2512.12071v1
• Date: Fri, 12 Dec 2025 22:33:26 GMT
• Title: Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles
• Authors: Takafumi Kita,
• Abstract summary: A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations.<n>An eigenvalue problem of a $$-rotation for a product of two operators is combined with an analysis on its rotational property to prove the connection.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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