The Dirac Equation And Its Solutions
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The Dirac Equation And Its Solutions
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Author : Vladislav G. Bagrov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-20
The Dirac Equation And Its Solutions written by Vladislav G. Bagrov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Science categories.
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In this monograph, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
The Supersymmetric Dirac Equation
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Author : Allen Hirshfeld
language : en
Publisher: World Scientific
Release Date : 2012
The Supersymmetric Dirac Equation written by Allen Hirshfeld and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Science categories.
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.
Relativistic Quantum Mechanics Of Leptons And Fields
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Author : W.T. Grandy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Relativistic Quantum Mechanics Of Leptons And Fields written by W.T. Grandy 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 material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study.
The Dirac Equation In Curved Spacetime
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Author : Peter Collas
language : en
Publisher: Springer
Release Date : 2019-03-29
The Dirac Equation In Curved Spacetime written by Peter Collas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-29 with Science categories.
This book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.
Exact Solutions Of Relativistic Wave Equations
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Author : V.G. Bagrov
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-02-28
Exact Solutions Of Relativistic Wave Equations written by V.G. Bagrov 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 1990-02-28 with Science categories.
'Et moi * .... si favait su comment en revenir. One service mathematics bllS rendered the je n'y serais point aile.' human race. It hal put common sense back Jules Verne where it bdongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
The Dirac Equation
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Author : Bernd Thaller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
The Dirac Equation written by Bernd Thaller 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 2013-12-01 with Science categories.
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.
Group Theoretical Foundations Of Quantum Mechanics
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Author : R. Mirman
language : en
Publisher: iUniverse
Release Date : 2005-05
Group Theoretical Foundations Of Quantum Mechanics written by R. Mirman and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05 with Mathematics categories.
Table of Contents Preface 1 Foundations 1 2 Why Geometry, so Physics, Require Complex Numbers 25 3 Properties of Statefunctions 38 4 The Foundations of Coherent Superposition 58 5 Geometry, Transformations, Groups and Observers 85 6 The Poincare Group and Its Implications 108 7 The Dimension of Space 122 8 Bosons, Fermions, Spinors and Orthogonal Groups 146 9 The Complete Reasonableness of Quantum Mechanics 159 A: Terminology and Conventions 177 The Einstein Podolsky Rosen Paradox 185 Experimental Meaning of the Concept of Identical Particles 191 Nonexistence of Superselection Rules; Definition of Term "Frame of Reference" 203 Complex Groups, Quantum Mechanics, and the Dimension and Reality of Space 221 The Reality and Dimension of Space and the Complexity of Quantum Mechanics 235 References 255 Index 259.
Relativistic Quantum Mechanics Wave Equations
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Author : Walter Greiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Relativistic Quantum Mechanics Wave Equations written by Walter Greiner 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 2013-03-09 with Science categories.
Relativistic Quantum Mechanics. Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course. This third edition has been slightly revised to bring the text up-to-date.
Analysis Of Dirac Systems And Computational Algebra
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Author : Fabrizio Colombo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of Dirac Systems And Computational Algebra written by Fabrizio Colombo 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 Mathematics categories.
* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics
Topological Insulators
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Author : Shun-Qing Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-11
Topological Insulators written by Shun-Qing Shen 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 2013-01-11 with Technology & Engineering categories.
Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.