Spinors In Four Dimensional Spaces
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Spinors In Four Dimensional Spaces
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Author : Gerardo F. Torres del Castillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Spinors In Four Dimensional Spaces written by Gerardo F. Torres del Castillo 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 2010-07-23 with Mathematics categories.
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.
Theory Of Spinors And Its Application In Physics And Mechanics
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Author : Vladimir A. Zhelnorovich
language : en
Publisher: Springer Nature
Release Date : 2019-10-24
Theory Of Spinors And Its Application In Physics And Mechanics written by Vladimir A. Zhelnorovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-24 with Science categories.
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.
Theory Of Spinors And Its Application In Physics And Mechanics
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Author : Vladimir Arkadʹevich Zhelnorovich
language : en
Publisher:
Release Date : 2019
Theory Of Spinors And Its Application In Physics And Mechanics written by Vladimir Arkadʹevich Zhelnorovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Spinor analysis categories.
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.
Spinors In Physics
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Author : Jean Hladik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spinors In Physics written by Jean Hladik 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.
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.
3 D Spinors Spin Weighted Functions And Their Applications
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Author : Gerardo F. Torres del Castillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-07
3 D Spinors Spin Weighted Functions And Their Applications written by Gerardo F. Torres del Castillo 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 2012-09-07 with Science categories.
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
The Theory Of Spinors
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Author : Elie Cartan
language : en
Publisher: Courier Corporation
Release Date : 1981-02-01
The Theory Of Spinors written by Elie Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-02-01 with Mathematics categories.
The French mathematician Élie Cartan (1869–1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity. One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value.
Complex Numbers The Higher Dimensional Forms 2nd Edition
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Author : Dennis Morris
language : en
Publisher: Createspace Independent Pub
Release Date : 2015-02-28
Complex Numbers The Higher Dimensional Forms 2nd Edition written by Dennis Morris and has been published by Createspace Independent Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-28 with Science categories.
This book is about the higher dimensional complex numbers. Although it was not known when the first edition was printed, the higher dimensional complex numbers are spinor spaces and the classical spaces, including our 4-dimensional space-time, arise from these spinor spaces by superimposition of isomorphic algebras. This book covers the mathematical foundations underlying the mathematics of spinors and the space-time of classical physics.To understand this book, the reader needs no more than an elementary understanding of matrices and an elementary understanding of finite group theory. Previous knowledge of complex numbers would be helpful.
On The Application Of Spinors To The Problems Of Celestial Mechanics
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Author : Karl Stumpff
language : en
Publisher:
Release Date : 1968
On The Application Of Spinors To The Problems Of Celestial Mechanics written by Karl Stumpff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Celestial mechanics categories.
Spinors And Space Time Volume 1 Two Spinor Calculus And Relativistic Fields
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Author : Roger Penrose
language : en
Publisher: Cambridge University Press
Release Date : 1984
Spinors And Space Time Volume 1 Two Spinor Calculus And Relativistic Fields written by Roger Penrose 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 1984 with Mathematics categories.
Volume 1 introduces and systematically develops the calculus in a first detailed exposition of this technique which provides shortcuts for some very tedious calculations.
Spinors In Hilbert Space
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Author : Paul Dirac
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spinors In Hilbert Space written by Paul Dirac 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.
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.