# Symmetry properties of non-Hermitian PT-symmetric quantum field theories

## TL;DR

This paper explores the symmetry properties of non-Hermitian PT-symmetric quantum field theories, revealing how conserved currents relate to transformations that do not leave the Lagrangian invariant, and examining implications for gauge theories and symmetry breaking.

## Contribution

It provides a detailed analysis of Noether's theorem in non-Hermitian PT-symmetric theories and extends understanding of gauge symmetry and spontaneous symmetry breaking in this context.

## Key findings

- Conserved currents in non-Hermitian theories correspond to non-invariant transformations.
- The Goldstone theorem and Higgs mechanism are applicable in PT-symmetric non-Hermitian frameworks.
- Insights into the formulation of gauge theories with non-Hermitian components.

## Abstract

We describe recent progress in understanding the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. Focussing on a simple non-Hermitian theory composed of one complex scalar and one complex pseudoscalar, we revisit the derivation of Noether's theorem to show that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. We illustrate the impact that this has on the consistent formulation of (Abelian) gauge theories by studying a non-Hermitian extension of scalar quantum electrodynamics. We consider the spontaneous breakdown of both global and local symmetries, and describe how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out for non-Hermitian, PT-symmetric theories.