Witten Index
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Supersymmetry In Quantum Mechanics
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Author : Fred Cooper
language : en
Publisher: World Scientific
Release Date : 2001
Supersymmetry In Quantum Mechanics written by Fred Cooper and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
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.
Supersymmetry In Quantum And Classical Mechanics
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Author : Bijan Kumar Bagchi
language : en
Publisher: CRC Press
Release Date : 2000-09-21
Supersymmetry In Quantum And Classical Mechanics written by Bijan Kumar Bagchi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-21 with Science categories.
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.
Index Theory Beyond The Fredholm Case
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Author : Alan Carey
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
Index Theory Beyond The Fredholm Case written by Alan Carey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case'. Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein's spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit computations on two examples: the Dirac operator in Rd, and a differential operator on an interval. Throughout, attention is paid to the history of the subject and earlier references are provided accordingly. The book is aimed at experts in index theory as well as newcomers to the field.
Supersymmetric Methods In Quantum And Statistical Physics
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Author : Georg Junker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Supersymmetric Methods In Quantum And Statistical Physics written by Georg Junker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
The Dawn Of The Lhc Era
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Author : Tao Han
language : en
Publisher: World Scientific
Release Date : 2010
The Dawn Of The Lhc Era written by Tao Han and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This book contains material from the lecture courses conducted at the Theoretical Advanced Study Institute (TASI, Colorado, USA) on high energy physics and cosmology in 2008. Three series of lectures are presented in parallel in the areas of Large Hadron Collider (LHC) phenomenology and experimentation; advanced theoretical topics beyond the standard model; and neutrino oscillation, astroparticle physics and cosmology. The phenomenology lectures cover a broad spectrum of standard research techniques used to interpret present-day and LHC data. The new physics lectures focus on modern speculations about physics beyond the standard model, with an emphasis on supersymmetry, grand unification theories, extra-dimensional theories, and string phenomenology, which may be tested at the LHC. The lecture series on neutrino physics, astroparticle physics and cosmology treats recent developments in neutrino oscillations, theories and searches of dark matter and dark energy, cosmic microwave background radiation, and density perturbation theory. The lectures are of pedagogical nature in presentation, and are accessible to advanced graduate students and researchers in high energy physics and cosmology.
Advanced Concepts In Particle And Field Theory
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Author : Tristan Hübsch
language : en
Publisher: Cambridge University Press
Release Date : 2023-02-09
Advanced Concepts In Particle And Field Theory written by Tristan Hübsch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.
This 2015 advanced textbook, now OA, provides students with a unified understanding of all matter at a fundamental level.
Supersymmetric Quantum Mechanics
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Author : Asim Gangopadhyaya
language : en
Publisher: World Scientific
Release Date : 2011
Supersymmetric Quantum Mechanics written by Asim Gangopadhyaya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
This is the first such text which will be directed to undergraduates. Our approach is to provide a self-contained exposition, which begins with a review of the relevant introductory quantum mechanics, then segues into SUSYQM. We concentrate on the essentials, both in the chapters developing the architecture, and in the later chapters of applications. While the text is designed to be accessible to undergraduate students, it should also be useful to graduate students and to researchers in the field. The text contains a large selection of examples and problems that illustrate the ideas and their applications. It is richly illustrated with figures that we have designed and produced. We have selected an attractive and relevant list of topics.
Supersymmetry
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Author : Pierre Binetruy
language : en
Publisher: OUP Oxford
Release Date : 2006-11-09
Supersymmetry written by Pierre Binetruy and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-09 with Science categories.
This book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios for supersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theory is needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.
Dynamical Groups And Spectrum Generating Algebras
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Author : Arno B?hm
language : en
Publisher: World Scientific
Release Date : 1988
Dynamical Groups And Spectrum Generating Algebras written by Arno B?hm and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This book contains comprehensive reviews and reprints on dynamical groups, spectrum generating algebras and spectrum supersymmetries, and their applications in atomic and molecular physics, nuclear physics, particle physics, and condensed matter physics. It is an important source for researchers as well as students who are doing courses on Quantum Mechanics and Advanced Quantum Mechanics.
Advanced Topics In Quantum Field Theory
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Author : Mikhail Shifman
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-28
Advanced Topics In Quantum Field Theory written by Mikhail Shifman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-28 with Science categories.
The Second Edition of this systematic, comprehensive text is revised to include topics developed in the last decade. A new final part presents more than 90 problems with detailed solutions, making this an indispensable book for graduate students and researchers in theoretical physics.