  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.
