Mathematics

 It is well known that the dynamics of a charged particle interacting with photons that are in a coherent state can, in good approximation, be described classically. Of course a coherent state is only an idealisation. But in which sense are the photons which are naturally created by a many body system of charged particles close to a coherent state? And is that enough to justify a classical behaviour? In the talk I will give an answer to these questions. I will discuss the solutions to the Pauli-Fierz equation, starting at time zero with a condensate of charges and no photons. I will show that the photons created in the course of the time evolution are indeed close to a coherent state and that their interaction with another charged particle can be described semiclassically, i.e., by means of the Schrödinger equation where the A-field is treated classically. I will also show, that A is a solution to Maxwell's equations.