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Author: Allen Hirshfeld Publisher: World Scientific ISBN: 1848167970 Category : Science Languages : en Pages : 216
Book Description
The solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book. Analysis of the concept of eccentricity of the orbits turns out to be essential to understanding the relation of the classical and quantum mechanical models. The opportunity is taken to relive the great moments of physics: From Kepler's discovery of the laws of motion of the planets the development is traced through the Dirac equation up to modern advances, which bring the concepts of supersymmetry to bear on the derivation of the solutions.
Author: Allen Hirshfeld Publisher: World Scientific ISBN: 1848167970 Category : Science Languages : en Pages : 216
Book Description
The solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book. Analysis of the concept of eccentricity of the orbits turns out to be essential to understanding the relation of the classical and quantum mechanical models. The opportunity is taken to relive the great moments of physics: From Kepler's discovery of the laws of motion of the planets the development is traced through the Dirac equation up to modern advances, which bring the concepts of supersymmetry to bear on the derivation of the solutions.
Author: Bernd Thaller Publisher: Springer Science & Business Media ISBN: 3662027534 Category : Science Languages : en Pages : 373
Book Description
Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all aspects cannot be done with sufficient depth within a single volume. In this book the emphasis is on the role of the Dirac equation in the relativistic quantum mechanics of spin-1/2 particles. We cover the range from the description of a single free particle to the external field problem in quantum electrodynamics. Relativistic quantum mechanics is the historical origin of the Dirac equation and has become a fixed part of the education of theoretical physicists. There are some famous textbooks covering this area. Since the appearance of these standard texts many books (both physical and mathematical) on the non relativistic Schrodinger equation have been published, but only very few on the Dirac equation. I wrote this book because I felt that a modern, comprehensive presentation of Dirac's electron theory satisfying some basic requirements of mathematical rigor was still missing.
Author: Georg Junker Publisher: Springer Science & Business Media ISBN: 364261194X Category : Science Languages : en Pages : 179
Book Description
The idea of supersymmetry was originally introduced in relativistic quantum field theories as a generalization of Poincare symmetry. In 1976 Nicolai sug gested an analogous generalization for non-relativistic quantum mechanics. With the one-dimensional model introduced by Witten in 1981, supersym metry became a major tool in quantum mechanics and mathematical, sta tistical, and condensed-IIll;l. tter physics. Supersymmetry is also a successful concept in nuclear and atomic physics. An underlying supersymmetry of a given quantum-mechanical system can be utilized to analyze the properties of the system in an elegant and effective way. It is even possible to obtain exact results thanks to supersymmetry. The purpose of this book is to give an introduction to supersymmet ric quantum mechanics and review some of the recent developments of vari ous supersymmetric methods in quantum and statistical physics. Thereby we will touch upon some topics related to mathematical and condensed-matter physics. A discussion of supersymmetry in atomic and nuclear physics is omit ted. However, the reader will find some references in Chap. 9. Similarly, super symmetric field theories and supergravity are not considered in this book. In fact, there exist already many excellent textbooks and monographs on these topics. A list may be found in Chap. 9. Yet, it is hoped that this book may be useful in preparing a footing for a study of supersymmetric theories in atomic, nuclear, and particle physics. The plan of the book is as follows.
Author: Fred Cooper Publisher: World Scientific ISBN: 9789810246129 Category : Science Languages : en Pages : 226
Book Description
This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by students in advanced undergraduate quantum mechanics courses. Problems have been given at the end of each chapter, along with complete solutions to all the problems. The text also includes material of interest in current research not usually discussed in traditional courses on quantum mechanics, such as the connection between exact solutions to classical solution problems and isospectral quantum Hamiltonians, and the relation to the inverse scattering problem.
Author: Georg Junker Publisher: Programme: Iop Expanding Physi ISBN: 9780750320245 Category : Science Languages : en Pages : 250
Book Description
Building on the earlier edition it now encapsulates the substantial developments that have been made in supersymmetric quantum mechanics in recent years. Aimed at graduate students and scientists this book provides a thorough review supersymmetric quantum mechanics and now includes problems and solutions.
Author: Asim Gangopadhyaya Publisher: World Scientific Publishing Company ISBN: 9813221062 Category : Science Languages : en Pages : 294
Book Description
We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of supersymmetric quantum mechanics. It is an outgrowth of a seminar course taught to physics and mathematics juniors and seniors at Loyola University Chicago, and of our own research over a quarter of a century.
Author: Daniel Z. Freedman Publisher: Cambridge University Press ISBN: 1139642855 Category : Science Languages : en Pages : 626
Book Description
Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Written by two of the most respected workers in the field, this is the first-ever authoritative and systematic account of supergravity. The book starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students, and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers. A website hosted by the authors, featuring solutions to some exercises and additional reading material, can be found at www.cambridge.org/supergravity.
Author: Bijan Kumar Bagchi Publisher: CRC Press ISBN: 9781420035810 Category : Science Languages : en Pages : 242
Book Description
Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.
Author: Michael Dine Publisher: Cambridge University Press ISBN: 113946244X Category : Science Languages : en Pages : 481
Book Description
The past decade has witnessed dramatic developments in the field of theoretical physics. This book is a comprehensive introduction to these recent developments. It contains a review of the Standard Model, covering non-perturbative topics, and a discussion of grand unified theories and magnetic monopoles. It introduces the basics of supersymmetry and its phenomenology, and includes dynamics, dynamical supersymmetry breaking, and electric-magnetic duality. The book then covers general relativity and the big bang theory, and the basic issues in inflationary cosmologies before discussing the spectra of known string theories and the features of their interactions. The book also includes brief introductions to technicolor, large extra dimensions, and the Randall-Sundrum theory of warped spaces. This will be of great interest to graduates and researchers in the fields of particle theory, string theory, astrophysics and cosmology. The book contains several problems, and password protected solutions will be available to lecturers at www.cambridge.org/9780521858410.
Author: Allen Hirshfeld
Author: Allen Hirshfeld
Author: Bernd Thaller
Author: Georg Junker
Author: Fred Cooper
Author: Georg Junker
Author: Asim Gangopadhyaya
Author: Daniel Z. Freedman
Author: Harald J W Muller-kirsten
Author: Bijan Kumar Bagchi
Author: Michael Dine