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Group Theory and the Many Body Problem

M. Moshińsky

Published Jan 1, 1968• 291 citations
OpenAlex

Abstract

Group theoretical techniques are pointed out which are effective for dealing with some many body problems. While Group Theory provides the backbone of all of the following discussion, vety little of its abstract formalism is used. The part used is either discussed in the text or the results for the group under discussion are stated pointing out the analogy between these results and those of the familiar rotation group. (auth)

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Group theoretical techniques are pointed out which are effective for dealing with some many body problems. While Group Theory provides the backbone of all of the following discussion, vety little of its abstract formalism is used. The part used is either discussed in the text or the results for the group under discussion are stated pointing out the analogy between these results and those of the familiar rotation group. (auth)
The auth ors review the application of the renormalisation group to many-body problems, with particular emphasis on the scaling behaviour which may arise. An introductory section discusses the difficulties of calculating the many-body effects near a magnetic phase transition, and shows by a simple example how the renormalisation group may be used to predict scaling behaviour. A general discussion of scaling and universality follows, with a review of techniques for calculation in lattice models, and an outline of the approaches in field theory. The range of applications of these techniques is discussed.
Abstract This book provides an introduction to quantum theory, primarily for mathematics students. It assumes a knowledge of basic algebra and elementary group theory, with little or no familiarity with more advanced topics. Although it takes a traditional approach, the book exploits ideas of linear algebra and points out some of the mathematical subtleties of the theory. It also covers such topics as Bell's inequalities and coherent and squeezed states, and introduces group representation theory, algebraic quantum theory, and quantum statistical mechanics. Later chapters discuss relativistic wave equations and elementary particle symmetries from a group-theoretical standpoint.