The Perturbation Theory

The essence of the theory of multiphoton processes proper lies in perturbation theory of one form or another. In this chapter we shall present a systematic development of perturbation theory and the relevant diagrammatic technique suitable for multiphoton processes. The simplest form of perturbation theory for multiphoton processes is that originally developed by Dirac(7) for studying, among other things, the interaction of radiation with matter. This method is suitable for both time-dependent and time-independent interactions. We shall first derive the multiphoton transition amplitudes using the (time-dependent) semiclassical interaction. Later we shall see that use of quantum-field interaction generates completely equivalent results for virtually all processes in laser fields. This circumstance allows one to treat most multiphoton processes in a laser field using either the semiclassical or quantum-field formalism; the choice depends mainly on convenience in any particular situation.