On the non-relativistic limit of charge conjugation in QED

TL;DR

This paper investigates the non-relativistic limit of charge conjugation in QED, showing that while C symmetry is broken in full QED, it can be well-defined when the electromagnetic field is classical and external, with implications for antihydrogen experiments.

Contribution

It extends previous work by deriving explicit expressions for charge conjugation operators for galilean electrons and positrons in an external electromagnetic field.

Findings

Charge conjugation limit exists with classical external fields.

Explicit C matrix and operator expressions for galilean electrons and positrons.

Relevance to recent antihydrogen experiments.

Abstract

Even if at the level of the non-relativistic limit of full QED, C is not a symmetry, the limit of this operation does exist for the particular case when the electromagnetic field is considered a classical external object coupled to the Dirac field. This result extends the one obtained when fermions are described by the Schroedinger-Pauli equation. We give the expressions for both the C matrix and the $\hat{C}$ operator for galilean electrons and positrons interacting with the external electromagnetic field. The result is relevant in relation to recent experiments with antihydrogen.