From Spinors to Quantum Mechanics

Author: Gerrit Coddens
Publisher: World Scientific
ISBN: 1783266392
Format: PDF, Mobi
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From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics. In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible. Contents: IntroductionIntroduction to GroupsSpinors in the Rotation GroupSpinors in the Homogeneous Lorentz GroupThe Dirac Equation from ScratchTowards a Better Understanding of Quantum MechanicsThe Hidden-Variables Issue and the Bell InequalitiesEquivalence of the Bohr-Sommerfeld and Dirac Theories for the Hydrogen AtomThe Problem of the Electron Spin within a Magnetic FieldThe Double-Slit Experiment and the Superposition PrincipleA Caveat About the Limitations of Group TheorySpin and Angular Momentum as Vector and Bi-Vector Concepts Readership: Graduate students and researchers in the field of quantum mechanics. Key Features:Offers an excellent introduction to the group theory coveredContains a new approach to the foundations of quantum mechanics, with some interesting resultsCorrects a number of mathematical errors in the existing literature, e.g. in relation with the anomalous g-factor of the electronKeywords:Group Theory;Quantum Mechanics;SU(2);SL(2,C);Dirac Equation

From Spinors to Quantum Mechanics

Author: Gerrit Coddens
Publisher:
ISBN: 9781783266364
Format: PDF, ePub, Mobi
Download Now
From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics. In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible.

The Theory of Spinors

Author: Élie Cartan
Publisher: Courier Corporation
ISBN: 0486137325
Format: PDF
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Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.

Quantum Theory Groups and Representations

Author: Peter Woit
Publisher: Springer
ISBN: 3319646125
Format: PDF
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This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Spinors in Physics

Author: Jean Hladik
Publisher: Springer Science & Business Media
ISBN: 1461214882
Format: PDF, Docs
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Invented by Dirac in creating his relativistic quantum theory of the electron, spinors are important in quantum theory, relativity, nuclear physics, atomic and molecular physics, and condensed matter physics. Essentially, they are the mathematical entities that correspond to electrons in the same way that ordinary wave functions correspond to classical particles. Because of their relations to the rotation group SO(n) and the unitary group SU(n), this discussion will be of interest to applied mathematicians as well as physicists.

Elements of Advanced Quantum Theory

Author: J. M. Ziman
Publisher: Cambridge University Press
ISBN: 9780521099493
Format: PDF, ePub, Mobi
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This textbook gives a connected mathematical derivation of the important mathematical results, concentrating on the central ideas without including elaborate detail or unnecessary rigour, and explaining in the simplest terms the symbols and concepts which confront the researcher in solid state, nuclear or high-energy physics.

Quantum Field Theory

Author: Lewis H. Ryder
Publisher: Cambridge University Press
ISBN: 9780521478144
Format: PDF, Docs
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This book is a modern introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the author develops the quantum theory of scalar and spinor fields, and then of gauge fields. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of "topological" objects in field theory and, new to this edition, a chapter devoted to supersymmetry. Graduate students in particle physics and high energy physics will benefit from this book.

Relativistic Quantum Mechanics and Field Theory

Author: Franz Gross
Publisher: John Wiley & Sons
ISBN: 3527617345
Format: PDF, Mobi
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An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.

Quantum Mechanics

Author: Askold M Perelomov
Publisher: World Scientific
ISBN: 9814495840
Format: PDF, Kindle
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It can serve as a good supplement to any quantum mechanics textbook, filling the gap between standard textbooks and higher-level books on the one hand and journal articles on the other. This book provides a detailed treatment of the scattering theory, multidimensional quasi-classical approximation, non-stationary problems for oscillators and the theory of unstable particles. It will be useful for postgraduate students and researchers who wish to find new, interesting information hidden in the depths of non-relativistic quantum mechanics. Contents: Discrete SpectrumContinuous SpectrumAnalytic Properties of Wave FunctionInverse Scattering ProblemThe Green Functions and Perturbation TheoryQuasi-classical ApproximationExact Solutions of Non-stationary Problems for OscillatorQuasi-stationary StatesAppendices:Specific Cases of the Schrödinger Equation SpectrumQuasi-classical Properties of Highly Excited Levels in the Coulomb Field Readership: Undergraduates, academics and researchers in physics. Keywords:Accidental Degeneracy;Bertrand Theorem;Coherent State;Coulomb Potential;Green Function;Inverse Scattering Problem;Isospectral Deformation;Perturbation Theory;Reflectionless Potential;Quantum Mechanics;Quasi-Classical Approximation;Quasi-Stationary State