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From Spinors To Quantum Mechanics
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Book Synopsis From Spinors To Quantum Mechanics by : Gerrit Coddens
Download or read book From Spinors To Quantum Mechanics written by Gerrit Coddens and published by World Scientific. This book was released on 2015-06-29 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spinors in Physics written by Jean Hladik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Spinors and Its Application in Physics and Mechanics by : Vladimir A. Zhelnorovich
Download or read book Theory of Spinors and Its Application in Physics and Mechanics written by Vladimir A. Zhelnorovich and published by Springer Nature. This book was released on 2019-10-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein–Dirac equations, nonlinear Heisenberg’s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.
Book Synopsis The Theory of Spinors by : Élie Cartan
Download or read book The Theory of Spinors written by Élie Cartan and published by Courier Corporation. This book was released on 2012-04-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spinors in Hilbert Space by : Paul Dirac
Download or read book Spinors in Hilbert Space written by Paul Dirac and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Hilbert Space The words "Hilbert space" here will always denote what math ematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable in finity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one.
Download or read book Not Even Wrong written by Peter Woit and published by Basic Books. This book was released on 2007-03-09 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: At what point does theory depart the realm of testable hypothesis and come to resemble something like aesthetic speculation, or even theology? The legendary physicist Wolfgang Pauli had a phrase for such ideas: He would describe them as "not even wrong," meaning that they were so incomplete that they could not even be used to make predictions to compare with observations to see whether they were wrong or not. In Peter Woit's view, superstring theory is just such an idea. In Not Even Wrong , he shows that what many physicists call superstring "theory" is not a theory at all. It makes no predictions, even wrong ones, and this very lack of falsifiability is what has allowed the subject to survive and flourish. Not Even Wrong explains why the mathematical conditions for progress in physics are entirely absent from superstring theory today and shows that judgments about scientific statements, which should be based on the logical consistency of argument and experimental evidence, are instead based on the eminence of those claiming to know the truth. In the face of many books from enthusiasts for string theory, this book presents the other side of the story.
Book Synopsis Introduction to Quantum Mechanics with Applications to Chemistry by : Linus Pauling
Download or read book Introduction to Quantum Mechanics with Applications to Chemistry written by Linus Pauling and published by Courier Corporation. This book was released on 2012-06-08 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic undergraduate text explores wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, and the structure of simple and complex molecules. Numerous tables and figures.
Book Synopsis Theory of Spinors and Its Application in Physics and Mechanics by : Vladimir Arkadʹevich Zhelnorovich
Download or read book Theory of Spinors and Its Application in Physics and Mechanics written by Vladimir Arkadʹevich Zhelnorovich and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein-Dirac equations, nonlinear Heisenbergs spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.
Book Synopsis From Spinors to Supersymmetry by : Herbi K. Dreiner
Download or read book From Spinors to Supersymmetry written by Herbi K. Dreiner and published by Cambridge University Press. This book was released on 2023-06-08 with total page 1031 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supersymmetry is an extension of the successful Standard Model of particle physics; it relies on the principle that fermions and bosons are related by a symmetry, leading to an elegant predictive structure for quantum field theory. This textbook provides a comprehensive and pedagogical introduction to supersymmetry and spinor techniques in quantum field theory. By utilising the two-component spinor formalism for fermions, the authors provide many examples of practical calculations relevant for collider physics signatures, anomalies, and radiative corrections. They present in detail the component field and superspace formulations of supersymmetry and explore related concepts, including the theory of extended Higgs sectors, models of grand unification, and the origin of neutrino masses. Numerous exercises are provided at the end of each chapter. Aimed at graduate students and researchers, this volume provides a clear and unified treatment of theoretical concepts that are at the frontiers of high energy particle physics.
Book Synopsis The Wonder of Quantum Spin by : Indubala I. Satija
Download or read book The Wonder of Quantum Spin written by Indubala I. Satija and published by Oxford University Press. This book was released on 2024-07-09 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wonder of Quantum Spin is a confection of the history and the science of quantum spin sprinkled with quotations and excerpts from pioneers who lived and breathed science. The book unfolds two centuries of the golden era in mathematics and physics, where first glimpses of spin appeared nearly 200 years ago in the mathematics of rotations. In these studies, spinors emerged as a new entity that changes sign after a 360 degree rotation, reminiscent of the Mobius geometry. A century later, quantum spins described by spinors was discovered in physics in atomic spectra. This led to the discovery of antimatter and raised the possibility of parity violation. It gave the first warning that protons and neutrons are not elementary. As we approach the centennial of the discovery, the spin mystique prevails as we have no clue of what exactly is spinning. Nevertheless, the theoretical framework underlying the spin determines why we exist, and explains the mysteries of the 3000-year-old phenomenon of magnetism. This book showcases MRI - one of the most important medical advances of the 20th century with a tantalizing history of the application of nuclear spin to humanity. It narrates fascinating spin tales of the precision measurements of electron and muon spin magnetic moments displaying a mindboggling confrontation between theory and experiment that remains our ambassador to quantum physics.
Book Synopsis Quantum Theory, Groups, Fields and Particles by : A. O. Barut
Download or read book Quantum Theory, Groups, Fields and Particles written by A. O. Barut and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry and Dynamics have played, sometimes dualistic, sometimes complimentary, but always a very essential role in the physicist's description and conception of Nature. These are again the basic underlying themes of the present volume. It collects self-contained introductory contributions on some of the recent developments both in mathematical concepts and in physical applications which are becoming very important in current research. So we see in this volume, on the one hand, differential geometry, group representations, topology and algebras and on the other hand, particle equations, particle dynamics and particle interactions. Specifically, this book contains a complete exposition of the theory of deformations of symplectic algebras and quantization, expository material on topology and geometry in physics, and group representations. On the more physical side, we have studies on the concept of particles, on conformal spinors of Cartan, on gauge and supersymmetric field theories, and on relativistic theory of particle interactions and the theory of magnetic resonances. The contributions collected here were originally delivered at two Meetings in Turkey, at Blacksea University in Trabzon and at the University of Bosphorus in Istanbul. But they have been thoroughly revised, updated and extended for this volume. It is a pleasure for me to acknowledge the support of UNESCO, the support and hospitality of Blacksea and Bosphorus Universities for these two memorable Meetings in Mathematical Physics, and to thank the Contributors for their effort and care in preparing this work.
Book Synopsis Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry by : Roger Penrose
Download or read book Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry written by Roger Penrose and published by Cambridge University Press. This book was released on 1984 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
Book Synopsis The Algebra of Spinors and Its Applications to Quantum Mechanics by : William Dickey Thacker
Download or read book The Algebra of Spinors and Its Applications to Quantum Mechanics written by William Dickey Thacker and published by . This book was released on 1978 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spinor Structures in Geometry and Physics by : V. M. Redkov
Download or read book Spinor Structures in Geometry and Physics written by V. M. Redkov and published by . This book was released on 2015 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to investigating the spinor structures in particle physics and in polarization optics. In fact, it consists of two parts joined by the question: Which are the manifestations of spinor structures in different branches of physics. It is based on original research. The main idea is the statement that the physical understanding of geometry should be based on physical field theories. The book contains numerous topics with the accent on field theory, quantum mechanics and polarization optics of the light, and on the spinor approach.
Author :Gerardo F. Torres del Castillo Publisher :Springer Science & Business Media ISBN 13 :0817681469 Total Pages :256 pages Book Rating :4.8/5 (176 download)
Book Synopsis 3-D Spinors, Spin-Weighted Functions and their Applications by : Gerardo F. Torres del Castillo
Download or read book 3-D Spinors, Spin-Weighted Functions and their Applications written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. It gives an introductory treatment of spinors. From the reviews: "Gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments. The book...should be appealing to graduate students and researchers in relativity and mathematical physics." -—MATHEMATICAL REVIEWS
Book Synopsis An Introduction To Quantum Field Theory by : Michael E. Peskin
Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Book Synopsis Relativistic Quantum Mechanics. Wave Equations by : Walter Greiner
Download or read book Relativistic Quantum Mechanics. Wave Equations written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
