Nonlinear Effects in Quantum Electrodynamics. Photon Propagation and Photon Splitting in an External Field

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Abstract
The effective nonlinear Lagrangian derived by Heisenberg and Euler is used to describe the propagation of photons in slowly varying but otherwise arbitrary electromagnetic fields. The group and the phase velocities for both propagation modes are calculated, and it is shown that the propagation is always causal. The photon splitting processes are also studied, and it is shown that they do not play any significant role even in very strong magnetic fields surrounding neutron stars.