Consistent description of field theories with non-Hermitian mass terms

TL;DR

This paper reviews how to formulate and analyze $PT$-symmetric field theories with non-Hermitian mass terms, emphasizing the role of discrete symmetries and conserved currents for model consistency.

Contribution

It provides a systematic review of $PT$-symmetric field theories with non-Hermitian masses, clarifying the role of symmetries and conserved quantities.

Findings

Discrete symmetries are crucial for model consistency.

The link between conserved currents and Lagrangian variations needs revision in continuous symmetries.

Guidelines for consistent $PT$-symmetric field theory formulation.

Abstract

We review how to describe a field theory that includes a non-Hermitian mass term in the region of parameter space where the Lagrangian is $PT$-symmetric. The discrete symmetries of the system are essential for understanding the consistency of the model, and the link between conserved current and variation of the Lagrangian has to be revisited in the case of continuous symmetries.