  The axion photon system in an external magnetic field, when the direction of
propagation of axions and photons is orthogonal to the direction of the
external magnetic field, displays a continuous axion-photon duality symmetry in
the limit the axion mass is neglected. The conservation law that follow in this
effective 2+1 dimensional theory from this symmetry is obtained. The magnetic
field interaction is seen to be equivalent to first order to the interaction of
a complex charged field with an external electric potential, where this
ficticious "electric potential" is proportional to the external magnetic field.
This allows one to solve for the scattering amplitudes using already known
scalar QED results. From the scalar QED analog the axion and the photon are
symmetric and antisymmetric combinations of particle and antiparticle. If one
considers therefore scattering experiments in which the two spatial dimensions
of the effective theory are involved non trivially, one observes that both
particle and antiparticle components of photons and axions are preferentially
scattered in different directions, thus producing the splitting or
decomposition of the photon and axion into their particle and antiparticle
components in an inhomogeneous magnetic field. This observable in principle
effect is of first order in the axion photon coupling, unlike the "light
shining through a wall phenomena ", which is second order.
