On The Concept Of Spinors In General Relativity
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Theory Of Spinors An Introduction
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Author : Moshe Carmeli
language : en
Publisher: World Scientific Publishing Company
Release Date : 2000-04-12
Theory Of Spinors An Introduction written by Moshe Carmeli and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-12 with Science categories.
Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.
Introduction To 2 Spinors In General Relativity
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Author : Peter J. O'Donnell
language : en
Publisher: World Scientific
Release Date : 2003
Introduction To 2 Spinors In General Relativity written by Peter J. O'Donnell and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter.
On The Concept Of Spinors In General Relativity
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Author : Werner Raab
language : en
Publisher:
Release Date : 1964
On The Concept Of Spinors In General Relativity written by Werner Raab and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
A spinor calculus is derived from tensor calculus and corresponds to the linear differential geometry based on four invariant linear differential forms. In the special theory of relativity, the concept 'system of coordinates' and 'frame' can be identified; in the general theory of relativity the system of coordinates which is common for all points of a certain space-time region has to be differentiated from the frame for every point. A frame is represented by four invariant linear differential forms, i.e. by four tensors of first rank.
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry
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Author : Roger Penrose
language : en
Publisher: Cambridge University Press
Release Date : 1984
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry 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.
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.
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.
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.
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 And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry
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Author : Roger Penrose
language : en
Publisher: Cambridge University Press
Release Date : 1986-02-27
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry 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 1986-02-27 with Science categories.
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. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.
Formulations Of General Relativity
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Author : Kirill Krasnov
language : en
Publisher: Cambridge University Press
Release Date : 2020-11-26
Formulations Of General Relativity written by Kirill Krasnov 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 2020-11-26 with Science categories.
This monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.
Spinors In General Relativity
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Author : Christopher James Grigson
language : en
Publisher:
Release Date : 1970
Spinors In General Relativity written by Christopher James Grigson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Quantum field theory categories.