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Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles
Takafumi Kita·December 12, 2025
Quantum Physicscond-mat.quant-gascond-mat.stat-mechcond-mat.str-elcond-mat.supr-con
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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 $π$-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.