My aim in this book has been to give an account of the theoretical methods of analysis of multiphoton processes in atomic physics. In this account I have emphasized systematic methods as opposed to ad hoc approaches. Both perturbative and nonperturbative methods are presented with il- lustrative results of concrete applications. The perturbation theory is the primary tool of analysis of nonresonant multiphoton processes. It is developed here in conjunction with a diagrammatic language and is also renormalized to free it from the unwanted divergences which accompany the ordinary treatment when higher-order corrections are considered. The nonperturbative methods (i.e., methods other than that of power series ex- pansion in the field strength) become particularly important for consistent treatments of problems involving, for example, intermediate resonances, high field strengths, and finite pulse duration. The specifically nonpertur- bative methods for multiphoton transitions are presented in Chapters 6-11. The methods of resolvent equations and of effective Hamiltonians are developed for both the stationary and the time-dependent fields.
The densi- ty matrix method is presented in conjunction with the problems of relaxa- tion and of fluctuating fields. The Floquet theory is presented both in the energy domain and in the time domain. Also treated are the methods of continued fractions, recursive iterative equations, and chain Hamiltonians.