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This user-friendly book on group theory introduces topics in as simple a manner as possible and then gradually develops those topics into more advanced ones, eventually building up to the current state-of-the-art. By using simple examples from physics and mathematics, the advanced topics become logical extensions of ideas already introduced. In addition to being used as a textbook, this book would also be useful as a reference guide for graduates and researchers in particle, nuclear and hadron physics.
applications to the structure of atomic nuclei. The author systematically develops these models from the elementary level, through an introduction to tensor algebra, to the use of group theory in spectroscopy. The book's extensive and detailed appendix includes a large selection of useful formulae of tensor algebra and spectroscopy. The serious graduate student, as well as the professional physicist, will find this complete treatment of the shell model to be an invaluable addition to the literature.
Organized in honor of K T Hecht, Professor of Physics at the University of Michigan, for his frontier research in group theory and nuclear physics, this symposium features papers by principal researchers who have contributed to the development and use of algebraic methods in nuclear physics. The symposium aims to make a critical assessment of what has been accomplished since the seminal work of J P Elliott on the SU(3) model, and to identify significant challenges and opportunities that lie in the future. Topics include the SU(3) model and its noncompact Sp(3, R) extension, boson and fermion dynamical symmetry schemes, pseudo-spin and superdeformation, cluster model configurations and calculations, recent advances in vector coherent state theories, quark models for subnucleon degrees of freedom in nuclei, and more.
This book is aimed at enabling the reader to obtain a working knowledge of the nuclear shell model and to understand nuclear structure within the framework of the shell model. Attention is concentrated on a coherent, self-contained exposition of the main ideas behind the model with ample illustrations to give an idea beyond formal exposition of the concepts. Since this text grew out of a course taught for advanced undergraduate and first-year graduate students in theoretical nuclear physics, the accents are on a detailed exposition of the material with step-by-step derivations rather than on a superficial description of a large number of topics. In this sense, the book differs from a number of books on theoretical nuclear physics by narrowing the subject to only the nuclear shell model. Most of the expressions used in many of the existing books treating the nuclear shell model are derived here in more detail, in a practitioner's way. Due to frequent student requests I have expanded of detail in order to take away the typical phrase " . . . after some the level simple and straightforward algebra one finds . . . ". The material could probably be treated in a one-year course (implying going through the problem sets and setting up a number of numerical studies by using the provided computer codes). The book is essentially self-contained but requires an introductory course on quantum mechanics and nuclear physics on a more general level.
In the present edition, a number of new features have been added. First of all, a number of typographical errors that had crept into the text have been corrected. More importantly, a number of new examples, figures and smaller sections have been added. In evaluating the two-body matrix elements which characterize the residual interaction, attention has been paid to the multipole expansion and insight into the importance of various multipoles is presented. The 18 example of 0 is now worked out for all the different angular momentum states in the section on configuration mixing. Some additional comments on how to determine one- and two-body matrix elements in jn configurations, on isospin and the application of isospin to the study of light odd-odd nuclei are included. In Chap. 3, a small section on the present use of large-scale shell model calculations and a section on experimental tests of how a nucleon actually moves inside the nucleus (using electromagnetic probing of nucleonic motion) has been added. In Chap. 4, some recent applications of the study of quadrupole motion in jn particle systems (with reference to the Po, Rn, Ra nuclei) are presented. In the discussion of magnetic dipole moments, the effects and importance of collective admixtures are pointed out and discussed. In Chap. 5, some small additions relating to the particle-hole conjugation and to the basic Hartree-Fock theory have been made. In Chap.
This book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics. It covers the applications of the group theory in various branches of physics and quantum chemistry, especially nuclear and molecular physics. Extensive tables and computational methods are presented.Group Representation Theory for Physicists may serve as a handbook for researchers doing group theory calculations. It is also a good reference book and textbook for undergraduate and graduate students who intend to use group theory in their future research careers.
Group Theory and Its Applications focuses on the applications of group theory in physics and chemistry. The selection first offers information on the algebras of lie groups and their representations and induced and subduced representations. Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems. The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy. The selection is a dependable reference for physicists and chemists interested in group theory and its applications.