Perturbative Methods in Field Theory

Abstract

In the preceding chapters, we have described several physical systems, photons, phonons, electron gas, nuclei, which we have treated by using semiquantitative methods: orders of magnitude, models, variational methods. The object of Chaps. 9 and 10 is to develop a more systematic method for calculating the effects of the interactions: the perturbation method. One finds that all the perturbative calculations used in field theory and in many-body problems proceed from the same common core, the time-dependent perturbative methods of quantum mechanics. At a strictly formal level, the method presents a large degree of generality. One must nevertheless take care not to abuse this apparent generality. While the basic formalism is unique, the applications are as diverse as the physical situations being considered. Thus, before beginning any significant perturbative calculation, it is necessary to consider the prerequisites of the physical effects and their orders of magnitude. The art of such a calculation resides in the judicious handling of a well-posed physical question. Before undertaking calculations, it is important to first determine the physical relevance of the expected results.