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Author: William McClain
Publisher: Springer Science & Business Media
ISBN: 0387734708
Category : Science
Languages : en
Pages : 672
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Book Description
Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.
Author: William McClain
Publisher: Springer Science & Business Media
ISBN: 0387734708
Category : Science
Languages : en
Pages : 672
Get Book Here
Book Description
Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.
Author: Wolfgang Ludwig
Publisher: Springer Science & Business Media
ISBN: 364297029X
Category : Science
Languages : en
Pages : 471
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Book Description
Everyone knows that symmetry is fundamentally important in physics. On one hand, the symmetry of a system is often the starting point for general physical considerations, and on the other hand, particular problems may be solved in simpler and more elegant ways if symmetry is taken into account. This book presents the underlying theories of symmetry and gives examples of their application in branches of physics ranging from solid-state to high-energy physics via atomic and molecular physics. The text is as self-contained as possible, with as much mathematical formalism given as required. The main emphasis is on the theory of group representations and on the method of projection operators, this is a very powerful tool which is often treated only very briefly. Discrete symmetries, continuous symmetries and symmetry breaking are also discussed, and exercises are provided to stimulate the reader to carry out original work.
Author: Jin-Quan Chen
Publisher: World Scientific
ISBN: 9812795421
Category : Mathematics
Languages : en
Pages : 287
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Book Description
This book is a tribute to the life and work of J Q Chen. The contributions of Chen to nuclear and molecular physics are discussed vis-a-vis present developments in these fields. Among other subjects, the present status of microscopic theories of the interacting boson model in nuclear physics and the theory of symmetry adaptation of molecular vibrations in molecular physics are reviewed. The latter theory is particularly useful for large molecular species such as fullerenes, where icosahedral symmetry plays a fundamental role. Contents: A Conceptual Review of the New Approach to Group Representation Theory (F Wang, Nanjing University, China); The Interacting Boson Model (P Van Isacker, GANIL, France); Structure of Nuclei Near the First Order Spherical-Deformed Phase Transition in the Interacting Boson Model (N V Zamfir, G E, Fernandes & R F Casten, Yale University, USA); Dynamical Symmetry Approach to Collective Motions in Many-Body Systems (C-L Wu, National Center for Theoretical Sciences, Taiwan); Fermion Dynamical Symmetries and High Temperature Superconductors (M Guidry, University of Tennessee, USA); Quantum Mechanics on a Sphere (J N Ginocchio, Los Alamos National Laboratory, USA); The Method of Symmetrized Bosons (F Iachello, Yale University, Connecticut); The Perturbed Dirac-Coulomb Problem via SO(2,1) Algebra. A Dilemma! (K T Hecht, University of Michigan, USA); Continuous Groups and Molecular Electronic Structure (J Paldus & X-Z Li); and other papers. Readership: Researchers in nuclear, molecular and mathematical physics."
Author: Bruno Gruber
Publisher: Springer Science & Business Media
ISBN: 1461529565
Category : Science
Languages : en
Pages : 613
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Book Description
The Symposium "Symmetries in Science VII: Spectrum Generating Algebras and Dynamic Symmetries in Physics" was held at the Southern Illinois University at Carbondale in Niigata, Japan Campus, during the period August 28-31, 1992. The Symposium was held in honor of Professor Francesco lachello on the occasion of his 50th birthday. We wish to thank the colleagues and friends of Franco for their participation in the Symposium as well as for contributing articles to this volume honoring him. It was their commitment and involvement which made this Symposium a success. We also wish to thank Dr. Jared H. Dorn, the director of SIUC-N, for his support in the planning and the execution of the Symposium. Moreover we wish to thank Mayor Nobuo Kumakura of Nakajo town and Mr. Kaichi Suzuki of the school entity "The Pacific" for their friendly support. Bruno Gruber, SIUC-N Takaharu Otsuka, University of Tokyo v LAUDATIO ON THE OCCASION OF THE 50TH BIRTHDAY OF PROFESSOR FRANCESCO IACHELLO I first met Franco lachello in 1974. Driving a smart Alfa-Romeo, he came to meet me at the station at Groningen where I was to spend a summer conducting research.
Author: J.P Gazeau
Publisher: CRC Press
ISBN: 9780750309332
Category : Mathematics
Languages : en
Pages : 1004
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Book Description
One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but also include such disciplines as chemistry and biology. Awarded the Wigner Medal and the Weyl Prize, respectively, H.J. Lipkin and E. Frenkel begin the volume with their contributions. Plenary session contributions are represented by 18 longer articles, followed by nearly 200 shorter articles. The book also presents coherent states, wavelets, and applications and quantum group theory and integrable systems in two separate sections. As a record of an international meeting devoted to the physical and mathematical aspects of group theory, GROUP 24: Physical and Mathematical Aspects of Symmetries constitutes an essential reference for all researchers interested in various current developments related to the important concept of symmetry.
Author: Teturo Inui
Publisher: Springer Science & Business Media
ISBN: 3642800211
Category : Science
Languages : en
Pages : 409
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Book Description
This book has been written to introduce readers to group theory and its ap plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.
Author: Wolfram Hergert
Publisher: John Wiley & Sons
ISBN: 352741133X
Category : Science
Languages : en
Pages : 387
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Book Description
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
Author: Klaus Mainzer
Publisher: Walter de Gruyter
ISBN: 3110886936
Category : Philosophy
Languages : en
Pages : 696
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Book Description
Author: Charles V. Benton
Publisher: Nova Publishers
ISBN: 9781590339398
Category : Mathematics
Languages : en
Pages : 286
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Book Description
Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. mechanics (both nonrelativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field. Structure of the Kalb-Ramond Gauge Symmetry and Spinor Representations; Group Theoretical Interpretation of CPT-Theorem; Cross Recurrence Plots and Their Applications; Analytical Solutions of the Radiative Transfer Equation in One-dimensional Spherical Geometry With Central Symmetry; Hyperspherical Functions and Harmonic Analysis on the Lorentz Group; The Next Stage: Quantum Game Theory; Index.
Author: John Ferraro
Publisher: Springer Science & Business Media
ISBN: 1468487957
Category : Mathematics
Languages : en
Pages : 294
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Book Description
The success of the first edition of this book has encouraged us to revise and update it. In the second edition we have attempted to further clarify por tions of the text in reference to point symmetry, keeping certain sections and removing others. The ever-expanding interest in solids necessitates some discussion on space symmetry. In this edition we have expanded the discus sion on point symmetry to include space symmetry. The selection rules in clude space group selection rules (for k = 0). Numerous examples are pro vided to acquaint the reader with the procedure necessary to accomplish this. Recent examples from the literature are given to illustrate the use of group theory in the interpretation of molecular spectra and in the determination of molecular structure. The text is intended for scientists and students with only a limited theoretical background in spectroscopy. For this reason we have presented detailed procedures for carrying out the selection rules and normal coor dinate treatment of molecules. We have chosen to exclude discussion on symmetry aspects of molecular orbital theory and ligand field theory. It has been our approach to highlight vibrational data only, primarily to keep the size and cost of the book to a reasonable limit.
