The anomalous spin-statistics connection arising from pseudo-Hermiticity

TL;DR

This paper introduces a novel spin-statistics theorem in pseudo-Hermitian quantum field theories, where the usual spin-statistics relationship is reversed due to the use of pseudo-Hermitian conjugation, while maintaining key physical properties.

Contribution

It establishes a new spin-statistics connection in pseudo-Hermitian quantum fields, challenging the conventional association between spin and statistics.

Findings

Integer spin fields exhibit fermionic statistics

Half-integer spin fields exhibit bosonic statistics

Locality, Lorentz covariance, and unitarity are preserved in free theories

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.