The anomalous spin-statistics connection arising from pseudo-Hermiticity

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.