Anomalies in 𝒫𝒯-Symmetric Quantum Field Theory

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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.

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