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arXiv · 2510.22952

The anomalous spin-statistics connection arising from pseudo-Hermiticity

Yao Bai·Cheng-Yang Lee·Ruifeng Leng·Siyi Zhou
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Abstract

We establish a new spin-statistics theorem for a class of free pseudo-Hermitian quantum field theories whose particles furnish unitary irreducible representations of the Poincar\'{e} group. In this framework, free pseudo-Hermitian fields with integer spin exhibit fermionic statistics, whereas those with half-integer spin exhibit bosonic statistics, opposite to the conventional case. This reversal arises from defining canonical field operators using pseudo-Hermitian conjugation rather than Hermitian conjugation, thereby circumventing the conventional spin-statistics theorem. The free fields retain locality, Lorentz covariance, and unitary evolution. However, interactions may violate unitarity due to the intrinsically non-Hermitian nature of the full Hamiltonian. We discuss potential resolutions to restore unitarity in interacting theories.

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Yao Bai, Cheng-Yang Lee, Ruifeng Leng, Siyi Zhou. 2025-10-27. The anomalous spin-statistics connection arising from pseudo-Hermiticity. https://arxiv.org/abs/2510.22952

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