Photon splitting in a laser field

Photon splitting due to vacuum polarization in a laser field is considered. Using an operator technique, we derive the amplitudes for arbitrary strength, spectral content and polarization of the laser field. The case of a monochromatic circularly polarized laser field is studied in detail and the amplitudes are obtained as three-fold integrals. The asymptotic behavior of the amplitudes for various limits of interest are investigated also in the case of a linearly polarized laser field. Using the obtained results, the possibility of experimental observation of the process is discussed.