Bosonic Spin-1 SOPHY

TL;DR

The paper addresses constructing and quantizing a second-order pseudo-Hermitian field theory (SOPHY) for a massive spin-1 field transforming in the (1,0)+(0,1) rep of the restricted Lorentz group, ensuring a real spectrum and unitary evolution through a metric η. The authors build the field from parity eigenvectors, implement a pseudo-Hermitian dual, demonstrate causality, and derive conserved charges and CPT-invariant discrete symmetries, while outlining renormalizable self-interactions and a Higgs-portal coupling that renders the lightest field a viable WIMP dark matter candidate. They argue the model provides a renormalizable, gauge-singlet spin-1 DM candidate with a rich RG structure and potential phenomenology via Higgs interactions, and point to generalizations to higher-spin SOPHY theories. These results establish a consistent framework for higher-spin SOPHYs and motivate further study of their phenomenology and UV behavior.

Abstract

In this work we study the canonical quantization of a second-order pseudo-Hermitian field theory for massive spin-1 bosons transforming under the $(1,0)\oplus(0,1)$ representation of the restricted Lorentz Group and satisfying the Klein-Gordon equation.