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

TL;DR

This paper develops a canonical quantization framework for spin-1/2 massive bosons satisfying the Klein-Gordon equation, introducing a pseudo-Hermitian structure that maintains physical consistency despite breaking the usual spin-statistics connection.

Contribution

It presents a novel quantization method for spin-1/2 bosons using pseudo-Hermitian operators, ensuring a bounded Hamiltonian and preserving fundamental symmetries.

Findings

Hamiltonian is bounded from below with real eigenvalues

Theory is consistent with microcausality and discrete symmetries

Breaks the usual spin-statistics connection due to dual field redefinition

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.