Spinors In Four Dimensional Spaces

Author : Gerardo F. Torres del Castillo
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 50,7 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9780817649845

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Spinors in Four-Dimensional Spaces by Gerardo F. Torres del Castillo Pdf

Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang–Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.

Author : Vladimir A. Zhelnorovich
Publisher : Springer Nature
Page : 392 pages
File Size : 47,6 Mb
Release : 2019-10-24
Category : Science
ISBN : 9783030278366

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Theory of Spinors and Its Application in Physics and Mechanics by Vladimir A. Zhelnorovich Pdf

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.

Author : Gerardo F. Torres del Castillo
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 55,9 Mb
Release : 2012-09-07
Category : Science
ISBN : 9780817681463

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3-D Spinors, Spin-Weighted Functions and their Applications by Gerardo F. Torres del Castillo Pdf

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

Author : Jean Hladik
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461214885

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Spinors in Physics by Jean Hladik Pdf

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.

Author : Vladimir Arkadʹevich Zhelnorovich
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 2019
Category : Spinor analysis
ISBN : 3030278379

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Theory of Spinors and Its Application in Physics and Mechanics by Vladimir Arkadʹevich Zhelnorovich Pdf

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.

Author : Roger Penrose,Wolfgang Rindler
Publisher : Cambridge University Press
Page : 516 pages
File Size : 48,8 Mb
Release : 1984
Category : Mathematics
ISBN : 0521347866

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Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry by Roger Penrose,Wolfgang Rindler Pdf

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.

Author : Andrzej Borowiec,Bernard Jancewicz,Zbigniew Oziewicz
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401117197

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Spinors, Twistors, Clifford Algebras and Quantum Deformations by Andrzej Borowiec,Bernard Jancewicz,Zbigniew Oziewicz Pdf

ZBIGNIEW OZIEWICZ University of Wroclaw, Poland December 1992 The First Max Born Symposium in Theoretical and Mathematical Phy sics, organized by the University of Wrodaw, was held in September 1991 with the intent that it would become an annual event. It is the outgrowth of the annual Seminars organized jointly since 1972 with the University of Leipzig. The name of the Symposia was proposed by Professor Jan Lopu szanski. Max Born, an outstanding German theoretical physicist, was born in 1883 in Breslau (the German name of Wrodaw) and educated here. The Second Max Born Symposium was held during the four days 24- 27 September 1992 in an old Sobotka Castle 30 km west of Wrodaw. The Sobotka Castle was built in the eleventh century. The dates engraved on the walls of the Castle are 1024, 1140, and at the last rebuilding, 1885. The castle served as a cloister until the end of the sixteenth century.

Author : Anonim
Publisher : Cambridge University Press
Page : 1030 pages
File Size : 40,8 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9780521800884

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From Spinors to Supersymmetry by Anonim Pdf

Author : Herbi K. Dreiner,Howard E. Haber,Stephen P. Martin
Publisher : Cambridge University Press
Page : 1031 pages
File Size : 46,9 Mb
Release : 2023-06-08
Category : Science
ISBN : 9781009347532

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From Spinors to Supersymmetry by Herbi K. Dreiner,Howard E. Haber,Stephen P. Martin Pdf

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.

Author : Élie Cartan
Publisher : Courier Corporation
Page : 192 pages
File Size : 42,5 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486137322

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The Theory of Spinors by Élie Cartan Pdf

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.

Author : L D Landau,E. M. Lifshitz
Publisher : Elsevier
Page : 382 pages
File Size : 43,9 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483187228

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Quantum Mechanics by L D Landau,E. M. Lifshitz Pdf

Quantum Mechanics deals with various aspects of quantum mechanics and covers topics ranging from the uncertainty principle and the principle of superposition to conservation laws, Schrödinger's equation, and perturbation theory. Spin, radiation, and the identity of particles are also discussed, along with the atom, the diatomic molecule, elastic and inelastic collisions, and Feynman diagrams. Comprised of 16 chapters, this volume begins with an overview of non-relativistic quantum theory and the basic concepts of quantum mechanics such as the principles of uncertainty and superposition, operators, and the density matrix. Subsequent chapters deal with conservation laws in quantum mechanics; Schrödinger's equation and general properties of its solutions; perturbations independent of time and dependent on time; spin and the spin operator; and the principle of indistinguishability of similar particles. The atom and its electron states are also examined, together with diatomic molecules; elastic and inelastic collisions; photons and electrons; Dirac's equation; and particles and antiparticles. The final chapter is devoted to Feynman diagrams, paying particular attention to the scattering matrix, radiative corrections, and radiative shift of atomic levels. This book will be of interest to physicists.

Author : Mariana Graña,Hagen Triendl
Publisher : Springer
Page : 74 pages
File Size : 50,9 Mb
Release : 2017-03-21
Category : Science
ISBN : 9783319543161

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String Theory Compactifications by Mariana Graña,Hagen Triendl Pdf

The lectures in this book provide graduate students and non-specialist researchers with a concise introduction to the concepts and formalism required to reduce the ten-dimensional string theories to the observable four-dimensional space-time - a procedure called string compactification. The text starts with a very brief introduction to string theory, first working out its massless spectrum and showing how the condition on the number of dimensions arises. It then dwells on the different possible internal manifolds, from the simplest to the most relevant phenomenologically, thereby showing that the most elegant description is through an extension of ordinary Riemannian geometry termed generalized geometry, which was first introduced by Hitchin. Last but not least, the authors review open problems in string phenomenology, such as the embedding of the Standard Model and obtaining de Sitter solutions.

Author : Pierre Deligne,Pavel Etingof,Daniel S. Freed,Lisa C. Jeffrey,David Kazhdan,John W. Morgan,David R. Morrison,Edward Witten
Publisher : American Mathematical Society
Page : 801 pages
File Size : 55,5 Mb
Release : 1999-10-25
Category : Mathematics
ISBN : 9780821820131

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Quantum Fields and Strings: A Course for Mathematicians by Pierre Deligne,Pavel Etingof,Daniel S. Freed,Lisa C. Jeffrey,David Kazhdan,John W. Morgan,David R. Morrison,Edward Witten Pdf

A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Author : Roger Penrose,Wolfgang Rindler
Publisher : Cambridge University Press
Page : 476 pages
File Size : 48,5 Mb
Release : 1984
Category : Mathematics
ISBN : 0521337070

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Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields by Roger Penrose,Wolfgang Rindler Pdf

Volume 1 introduces and systematically develops the calculus in a first detailed exposition of this technique which provides shortcuts for some very tedious calculations.

Author : Paolo Budinich,Andrzej Trautman
Publisher : Springer Science & Business Media
Page : 136 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642834073

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The Spinorial Chessboard by Paolo Budinich,Andrzej Trautman Pdf

Spinor theory is an important tool in mathematical physics in particular in the context of conformal field theory and string theory. These lecture notes present a new way to introduce spinors by exploiting their intimate relationship to Clifford algebras. The presentation is detailed and mathematically rigorous. Not only students but also researchers will welcome this book for the clarity of its style and for the straightforward way it applies mathematical concepts to physical theory.