Classical solutions in quantum field theory. Solitons and instantons in high energy physics.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1264.81009
DOI: 10.1017/CBO9781139017787.001
author: Erick J. Weinberg
publication date: 2012-08-16T00:00:00Z
Mathematics Subject Classification ID: 81-01
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 14D21
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 6066605
zbMATH Keywords: solitons
zbMATH Keywords: instantons
zbMATH Keywords: magnetic monopoles
MaRDI profile type: Publication
full work available at URL: cbo9781139017787.001
OpenAlex ID: W2343618010
title: Classical solutions in quantum field theory. Solitons and instantons in high energy physics.
published in: Cambridge Monographs on Mathematical Physics
review text: 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.
reviewed by: Gert Roepstorff
description: scientific article; zbMATH DE number 6066605