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

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.