Representation of Charge Conjugation for Dirac Fields

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Abstract
Explicit representations of the charge conjugation transformation for fermion fields are derived in a form which does not make explicit reference to the expansion of the fields in a complete orthonormal set of space and spin functions. It is shown that the different forms must be equivalent if one is working in an irreducible representation of the Wigner-Jordan anticommutation rules, but it has not been found possible to prove the equivalence directly, thus suggesting that the representations are not equivalent if the representation of the anticommutation relations is not irreducible. The results are applied to the clarification of an apparent paradox concerning commutability of the charge conjugation and space inversion transformations.