On the non-relativistic limit of charge conjugation in QED

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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 C operator for galilean electrons and positrons interacting with the external electromagnetic field. The result is relevant in relation to recent experiments with antihydrogen.