This book is the result of a graduate-level "special topics" course I gave at the University of Rochester in 1970. The purpose of the course was to discuss as far as possible all known symmetries in nuclei, with special emphasis on dynamical symmetries. Since there was no comprehensive account of this subject in the literature, I was encouraged to write a review based on my lecture notes. The end result is the present volume. Like the course, the book is intended mainly for graduate students and research workers in nuclear physics. The only prior knowledge required to follow the book is graduate-level quantum mechanics and nuclear physics and hence I believe that it can be useful to both experimental and theoretical nuclear physicists. In addition, the book should prepare a student to read the latest literature on the subject and also train him to do group theoretic work in nuclear physics. The organization of the material in the book is described in Chapter 1.

This book provides an understandable review of SU(3) representations, SU(3) Wigner–Racah algebra and the SU(3) ⊃ SO(3) integrity basis operators, which are often considered to be difficult and are avoided by most nuclear physicists. Explaining group algebras that apply to specific physical systems and discussing their physical applications, the book is a useful resource for researchers in nuclear physics. At the same time it helps experimentalists to interpret data on rotational nuclei by using SU(3) symmetry that appears in a variety of nuclear models, such as the shell model, pseudo-SU(3) model, proxy-SU(3) model, symplectic Sp(6, R) model, various interacting boson models, various interacting boson–fermion models, and cluster models. In addition to presenting the results from all these models, the book also describes a variety of statistical results that follow from the SU(3) symmetry.

This volume gives a borad overview on symmetry methods ypplied to molecular and nuclear physics, to particle physics, decay processes, and phase space dynamics. The thoroughly edited contributions should be of interest not only to scientists but also to thos that want to see how symmetry considerations are put to work in twentieth century physics.

This book is devoted to algebraic models and their applications. It presents a simple, but thorough, pedagogic approach, starting from the most elementary ideas and building up to the most recent results of advanced theories. The book is designed for a graduate level treatment.

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.