Classical solutions in quantum field theory. Solitons and instantons in high energy physics.
Erick Weinberg has worked over the years on instantons, solitons, and many of their applications for high energy physics. His research interests also include topics in cosmology. He has now written this book for advanced graduate students, which is, in fact, a remarkable survey and offers a general overview of this field. Solitons, magnetic monopoles, and instantons arise as classical solutions to quantum field equations, providing a fascinating topic of mathematical physics. Much of the book is devoted to this aspect. However, the main aim of this book is to provide a self-contained introduction and an up-to-date survey on many aspects of classical solutions. It starts with a discussion of one-dimensional solitons, because working in one dimension simplifies the analysis, followed by a chapter on solitons in more than one dimension. Then the 't Hooft-Polyakov monopole within the context of a U(1) gauge group and other magnetic mopoles within larger gauge groups are discussed, followed by possible cosmological implications: the evolution of the primordial monopole abundance. BPS solitons and Yang-Mills instantons are the next topic. Euclidean instantons give rise to nonperturbative effects, while Euclidean bounce solutions govern transition between metastable states. Finally, false vacua and vacuum decay are the topic of the final chapter. Through careful writing this monograph achieves much more than what has been published before and may be considered, in fact, a new and very important book.
scientific article; zbMATH DE number 6066605