Second-order pseudo-Hermitian spin-$1/2$ bosons

TL;DR

This work addresses describing massive spin-$\tfrac{1}{2}$ bosons that satisfy the Klein-Gordon equation by employing a second-order pseudo-Hermitian (SOPHY) formalism, where Hermiticity is replaced by pseudo-Hermiticity via an $\eta$ operator. The authors construct a consistent canonical quantization that yields a real energy spectrum, preserves microcausality, and respects $P$, $C$, and $T$ symmetries, despite the unconventional spin-statistics relation. The theory features eight degrees of freedom and mass dimension one, realized through a doubling of Dirac fields, and admits renormalizable self-interactions and Higgs-portal couplings, enabling dark matter phenomenology. Overall, the SOPHY framework provides a simple, consistent extension of pseudo-Hermitian QFT to a spin-$\tfrac{1}{2}$ system, with potential implications for RG studies and beyond-Standard-Model model-building.

Abstract

The canonical quantization of a field theory for spin-$1/2$ massive bosons that satisfy the Klein-Gordon equation is presented. The breakdown of the usual spin-statistics connection is due to the redefinition of the dual field, rendering the theory pseudo-Hermitian. The normal-ordered Hamiltonian is bounded from below with real eigenvalues, and the theory is consistent with microcausality and invariant under parity, charge conjugation and time reversal.