  We observe that it is very usefull to introduce a complex field for the axion
photon system in an external magnetic field, when for example considered with
the geometry of the experiments exploring axion photon mixing, where the real
part is the axion and the imaginary part is the photon polarization that
couples to the axion when the magnetic field is present. In the absence of the
external magnetic field, the theory displays charge conjugation symmetry. In
this formulation the axion and photon are the symmetric and antisymmetric
combinations of particle and antiparticle (as defined from the complex field)
respectively and they do not mix if the external magnetic field is set to zero.
The magnetic field interaction is seen to be equivalent to first order to the
interaction of the complex charged field with an external electric potential,
where this ficticious "electric potential" is proportional to the external
magnetic field. This interaction breaks the charge conjugation symmetry and
therefore symmetric and antysymmetric combinations are not mantained in time.
As a result one obtains axion photon mixing in the presence of an external
magnetic field, a well known result understood in a different way.
