Non-Hermiticity: a new paradigm for model building in particle physics

TL;DR

This paper reviews recent advances in non-Hermitian quantum field theories, emphasizing their unique features, symmetries, and potential for constructing non-Hermitian extensions of the Standard Model in particle physics.

Contribution

It introduces the formulation of non-Hermitian quantum field theories, explores their symmetries, and discusses their application to model building beyond the Standard Model.

Findings

Non-Hermitian theories exhibit unique discrete symmetries.

Extensions include non-Hermitian supersymmetric and gauge theories.

Potential implications for neutrino sector modeling.

Abstract

Non-Hermitian quantum theories have been applied in many other areas of physics. In this note, I will briefly review recent developments in the formulation of non-Hermitian quantum field theories, highlighting features that are unique compared to Hermitian theories. I will touch upon their crucial discrete symmetries and how continuous symmetry properties are borne out, including Noether's theorem, the Goldstone theorem and the Englert-Brout-Higgs mechanism. As examples, I will describe a non-Hermitian supersymmetric theory, and draw attention to non-Hermitian deformations of (scalar) QED, the Higgs-Yukawa theory and flavour oscillations, with potential implications for non-Hermitian model building in the neutrino sector. Together, these results pave the way for a systematic programme for building non-Hermitian extensions of the Standard Model of particle physics.