Soft Quanta

Centre d’Études Nucléaires de Saclay, B. P. n° 2 — F 91 - Gif-sur-Yvette, France.

Abstract

These notes are based on some work done in collaboration with H. Abarbanel. He cannot, however, be held responsible for the present version. Our aim has been to get a better understanding of the relationship between quantum and classical electrodynamics, especially in view of the classical aspects of the infrared divergence. Much remains to be done and we can only hope to arouse some interest for these questions.

The material presented here is divided into three parts. Chapter I is a review of the classical theory of a point charge interacting with an external held. The emphasis is on the origin of the self-interaction term in the equation of motion, following the ideas of Dirac in his 1938 paper.

Chapter II contains a heuristic introduction to the corresponding quantum theory. A physical discussion of the infrared divergence leads to the study of the singularities of Green’s function. Our approach here is strongly influenced by the work of Schwinger, and more recently, by the thorough mathematical analysis of Kibble.

Chapter III uses the previous techniques and ideas to give a short discussion of the classical (or eikonal) approximation in non-relativistic and relativistic scattering theory.

We have included as many examples as possible, some being left merely as exercises for the patient reader. Each chapter ends with a short list of references. On the whole, the level of the discussion has been kept (hopefully) as elementary as possible so as to be of value to the students rather than to the specialists in the held. Thus we have not hesitated (with due reference) to reproduce some material available in the literature.

Résumé

Nous présentons une brève revue des relations de l’électromagnétisme classique et quantique. Un outil simplifié permet cette transition, c’est l’approximation dite « classique ». On en examine ici divers aspects. Tout d’abord on discute des effets de basse énergie et en premier chef la divergence infrarouge. Puis on passe à des approximations nouvelles en physique des hautes énergies où Ton trouve la forme asymptotique des amplitudes de diffusion pour les forces à longue portée comme les forces électromagnétiques.