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

Takafumi Kita

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arXiv · 2512.12071

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

Takafumi Kita

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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 $\pi$-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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quant-ph cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el cond-mat.supr-con

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Takafumi Kita. 2025-12-12. Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles. https://arxiv.org/abs/2512.12071

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