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Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2

Point form relativistic quantum mechanics
William H Klink, Wolfgang Schweiger


This book is the second in a series of volumes looking at what particular relativity is applicable to a given dynamical theory. This volume takes the point of view of a particle theory, based on the irreducible representations of the Poincare group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; we develop what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way.

A central issue in any relativistic quantum theory is how to introduce interactions without spoiling relativistic invariance. We show that interactions can be incorporated in a mass operator, in such a way that relativistic invariance is maintained. Surprisingly, for a relativistic theory, such a construction allows for instantaneous interactions; in addition, dynamical particle exchange and particle production can be included in a multichannel formulation of the mass operator. For systems of more than two particles, however, straightforward application of such a construction leads to the undesirable property that clusters of widely separated particles continue to interact with one another, even if the interactions between the individual particles are of short range. A significant part of this volume deals with the solution of this problem. 

Since relativistic quantum mechanics is not as well known as relativistic quantum field theory, a chapter is devoted to applications of point form quantum mechanics to nuclear physics; in particular, we show how constituent quark models can be used to derive electromagnetic and other properties of hadrons.

About Editors

William Klink received his PhD from Johns Hopkins University. He was professor of physics for many years at the University of Iowa, and is now professor emeritus. His main research interests have centred around the study of symmetry, both in its mathematical formulations, and in its physical consequences.

Wolfgang Schweiger received his PhD from the University of Graz, Austria. After a few postdoc years in Germany, he went back to Graz where he is now associate professor of theoretical physics. The main research activities concentrate on the theoretical treatment of few body problems in low- and intermediate-energy hadron physics by means of relativistic quantum mechanics and QCD perturbation theory. Further research interests include classically integrable systems such as soliton equations.

Table of Contents


Paperback ISBN: 9780750329057

Ebook ISBN: 9781681748900

DOI: 10.1088/978-1-6817-4891-7

Publisher: Morgan & Claypool Publishers


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