An Introduction to Spinors and Geometry with Applications in Physics PDF Download
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Author: Ian M. Benn
Publisher: Institute of Physics Publishing (GB)
ISBN:
Category : Mathematics
Languages : en
Pages : 376
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Book Description
"...The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory..."--back cover.
Author: Ian M. Benn
Publisher: Institute of Physics Publishing (GB)
ISBN:
Category : Mathematics
Languages : en
Pages : 376
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Book Description
"...The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory..."--back cover.
Author: Jayme Vaz Jr.
Publisher: Oxford University Press
ISBN: 0198782926
Category : Mathematics
Languages : en
Pages : 257
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Book Description
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.
Author: Peter J. O'Donnell
Publisher: World Scientific
ISBN: 9812383077
Category : Science
Languages : en
Pages : 205
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Book Description
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.
Author: Élie Cartan
Publisher: Courier Corporation
ISBN: 0486137325
Category : Mathematics
Languages : en
Pages : 193
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Book Description
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: Donal J. Hurley
Publisher: Springer
ISBN: 1852332239
Category : Science
Languages : en
Pages : 392
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Book Description
This text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.
Author: Roger Penrose
Publisher: Cambridge University Press
ISBN: 9780521347860
Category : Mathematics
Languages : en
Pages : 516
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Book Description
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: Pertti Lounesto
Publisher: Cambridge University Press
ISBN: 0521005515
Category : Mathematics
Languages : en
Pages : 352
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Book Description
This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.
Author: H. Blaine Lawson
Publisher: Princeton University Press
ISBN: 1400883911
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Author: S. A. Huggett
Publisher: Cambridge University Press
ISBN: 9780521456890
Category : Mathematics
Languages : en
Pages : 196
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Book Description
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.
Author: D.H. Sattinger
Publisher: Springer Science & Business Media
ISBN: 1475719108
Category : Mathematics
Languages : en
Pages : 218
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Book Description
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
