Vacuum polarization in laser fields

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Abstract
According to quantum electrodynamics the vacuum shows polarization properties because of the presence of virtual electron-positron pairs. These properties are investigated in the presence of an intense plane wave field, such as is produced by a laser. The laser wave is considered as an external prescribed field and its interaction with the electron-positron field is treated without reference to perturbation theory. The vacuum polarization tensor is computed to second order in the fine structure constant in the form of a double integral. For a Dyson equation for the photon propagator is solved by an eigenfunction expansion. For a plane laser wave of infinite extent and circular polarization the results are relatively simple and explicit. Analytical properties of the photon propagator are discussed. The effects of vacuum polarization on an additional weak wave field (a non-laser photon) can be described approximately by two complex indices of refraction.