Axion in an External Electromagnetic Field

We investigate the effective interaction of a pseudoscalar particle with two photons in an external electromagnetic field in the general case of all external particles being off the mass shell. This interaction is used to study the radiative decay $a \to \gamma \gamma$ of the axion, a pseudoscalar particle associated with the Peccei-Quinn symmetry, and the crossing channel of photon splitting $\gamma \to \gamma a$. It is shown that the external field removes the suppression associated with the smallness of the axion mass and so leads to the strong catalysis of these processes. The field-induced axion emission by photon is analyzed as one more possible source of energy losses by astrophysical objects.