Anomalies in PT-Symmetric Quantum Field Theory

TL;DR

This paper investigates PT-symmetric quantum field theories, revealing anomalies in a specific axial-vector coupling model and proposing an alternative with reversed PT properties that appears more promising.

Contribution

It identifies anomalies in a PT-symmetric electrodynamics model and introduces a new theory with reversed PT transformation properties that may be more consistent.

Findings

The axial-vector PT-symmetric model has anomalies and is nonrenormalizable.

An alternative vector current model with reversed PT properties is proposed.

The new model exhibits attractive theoretical features.

Abstract

It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.