Classical Solutions in Gauge Theories — Spherically Symmetric Monopoles — Lax Pairs and Toda Lattices

Abstract

The composite title deserves an explanation. I gave two lectures under the general title of “classical solutions in gauge theories”. Much of the material was introductory in nature and has been used in lectures to other audiences and has already been published(1,2,3,4,5), and therefore I propose to summarize it rather than repeat the details in print. The last quarter was devoted to the subject “Spherically symmetric monopoles — Lax Pairs- and Toda Lattices”. This topic has developed recently and brings together ideas from different branches of theoretical physics and mathematics. I feel it is an extremely important development, so far rather inaccessible, and I want to try to make it available to the wider audience it deserves by treating it at some length.