The Theory of Spinors

The Theory of Spinors
Author :
Publisher : Courier Corporation
Total Pages : 193
Release :
ISBN-10 : 9780486137322
ISBN-13 : 0486137325
Rating : 4/5 (22 Downloads)

Synopsis The Theory of Spinors by : Élie Cartan

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.

The Theory of Spinors

The Theory of Spinors
Author :
Publisher : Courier Corporation
Total Pages : 198
Release :
ISBN-10 : 0486640701
ISBN-13 : 9780486640709
Rating : 4/5 (01 Downloads)

Synopsis The Theory of Spinors by : Elie Cartan

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.

Theory of Spinors and Its Application in Physics and Mechanics

Theory of Spinors and Its Application in Physics and Mechanics
Author :
Publisher : Springer Nature
Total Pages : 402
Release :
ISBN-10 : 9783030278366
ISBN-13 : 3030278360
Rating : 4/5 (66 Downloads)

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

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.

The Algebraic Theory of Spinors and Clifford Algebras

The Algebraic Theory of Spinors and Clifford Algebras
Author :
Publisher : Springer Science & Business Media
Total Pages : 232
Release :
ISBN-10 : 3540570632
ISBN-13 : 9783540570639
Rating : 4/5 (32 Downloads)

Synopsis The Algebraic Theory of Spinors and Clifford Algebras by : Claude Chevalley

In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.

Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry

Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry
Author :
Publisher : Cambridge University Press
Total Pages : 516
Release :
ISBN-10 : 0521347866
ISBN-13 : 9780521347860
Rating : 4/5 (66 Downloads)

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

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.

Spinors in Physics

Spinors in Physics
Author :
Publisher : Springer Science & Business Media
Total Pages : 228
Release :
ISBN-10 : 9781461214885
ISBN-13 : 1461214882
Rating : 4/5 (85 Downloads)

Synopsis Spinors in Physics by : Jean Hladik

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.

Introduction to 2-spinors in General Relativity

Introduction to 2-spinors in General Relativity
Author :
Publisher : World Scientific
Total Pages : 205
Release :
ISBN-10 : 9789812383075
ISBN-13 : 9812383077
Rating : 4/5 (75 Downloads)

Synopsis Introduction to 2-spinors in General Relativity by : Peter J. O'Donnell

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.

From Spinors To Quantum Mechanics

From Spinors To Quantum Mechanics
Author :
Publisher : World Scientific
Total Pages : 404
Release :
ISBN-10 : 9781783266395
ISBN-13 : 1783266392
Rating : 4/5 (95 Downloads)

Synopsis From Spinors To Quantum Mechanics by : Gerrit Coddens

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.

An Introduction to Twistor Theory

An Introduction to Twistor Theory
Author :
Publisher : Cambridge University Press
Total Pages : 196
Release :
ISBN-10 : 0521456894
ISBN-13 : 9780521456890
Rating : 4/5 (94 Downloads)

Synopsis An Introduction to Twistor Theory by : S. A. Huggett

Evolving from graduate lectures given in London and Oxford, this introduction to twistor theory and modern geometrical approaches to space-time structure will provide graduate students with the basics of twistor theory, presupposing some knowledge of special relativity and differenttial geometry.

An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors
Author :
Publisher : Oxford University Press
Total Pages : 257
Release :
ISBN-10 : 9780198782926
ISBN-13 : 0198782926
Rating : 4/5 (26 Downloads)

Synopsis An Introduction to Clifford Algebras and Spinors by : Jayme Vaz Jr.

This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.