Quantum Electrodynamics in Strong Magnetic Fields. II. Photon Fields and Interactions

Abstract

A theory is developed which synthesizes the classical theory of wave-wave interactions in a medium and the QED theory of photon-photon interactions in a vacuum with or without static fields. First, a covariant version of the theory of wave dispersion in an arbitrary medium is outlined. Then the photon propagator is calculated both by solving the wave equation directly and from the vacuum expectation value, and the latter is generalized by introducing a statistically averaged propagator. The hierarchy of nonlinear responses of the medium is introduced and used to define a nonlinear interaction Hamiltonian. The expansion of the S matrix with this interaction Hamiltonian is re-ordered to correspond to a hierarchy of processes ordered according to the number of external photons. The theory is used to treat three-wave and four-wave interactions and both classical and QED applications are discussed. A covariant form of the Onsager relations and calculations of the hierarchy of response tensors using covariant classical kinetic theory and the Heisenberg-Euler Lagrangian are presented in appendices.