The Perturbation Theory

Abstract

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.