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Clifford Algebras & Spinors 2ND Edition

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Clifford Algebras & Spinors 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

This second edition of a popular and unique introduction to Clifford algebras and spinors has three new chapters. The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalized to higher dimensions.

Book News Annotation:

Beginning chapters, suited for undergraduates, introduce vectors, complex numbers, and quaternions as background for material on Clifford algebras. Later chapters, also of interest physicists, treat the quantum mechanics of the electron, electromagnetism, and special relativity. Recent research on Clifford algebras is surveyed, and a new classification of spinors is introduced, based on bilinear covariants of physical observables. Scalar products of spinors are classified by involuntary anti-automorphisms of Clifford algebras. Brauer-Wall groups and Witt rings are discussed, and Cauchy's integral formula is generalized to higher dimensions. The author is affiliated with Helsinki Polytechnic Stadia.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors.

Synopsis:

This is the second edition of Professor Lounesto's introduction to Clifford algebras and spinors.

Synopsis:

Here, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. This will interest physicists as well as mathematicians, and includes treatments of the quantum mechanics of the electron, electromagnetism and special relativity with Clifford algebras.

Synopsis:

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.

Table of Contents

Preface; Mathematical notation; 1. Vectors and linear spaces; 2. Complex numbers; 3. Bivectors and the exterior algebra; 4. Pauli spin matrices and spinors; 5. Quaternions; 6. The fourth dimension; 7. The cross product; 8. Electromagnetism; 9. Lorentz transformations; 10. The Dirac equation; 11. Fierz identities and boomerangs; 12. Flags, poles and dipoles; 13. Tilt to the opposite metric; 14. Definitions of the Clifford algebra; 15. Witt rings and Brauer groups; 16. Matrix representations and periodicity of 8; 17. Spin groups and spinor spaces; 18. Scalar products of spinors and the chessboard; 19. Möbius transformations and Vahlen matrices; 20. Hypercomplex analysis; 21. Binary index sets and Walsh functions; 22. Chevalley's construction and characteristic 2; 23. Octonions and triality; A history of Clifford algebras; Selected reading; Index.

Product Details

ISBN:
9780521005517
Editor:
Cassels, J. W. S.
Editor:
Hitchin, N. J.
Editor:
Cassels, J. W. S.
Editor:
Hitchin, N. J.
Author:
Lounesto, Pertti
Author:
Cassels, J. W. S.
Publisher:
Cambridge University Press
Location:
Cambridge, U.K.
Subject:
General
Subject:
Probability
Subject:
Algebra - General
Subject:
Algebra - Linear
Subject:
Spinor analysis
Subject:
Clifford algebras
Subject:
Probability & Statistics - General
Subject:
Clifford algebras Clifford algebras
Subject:
Mathematics-Linear Algebra
Edition Number:
2
Edition Description:
Trade paper
Series:
London Mathematical Society Lecture Note Series
Series Volume:
239
Publication Date:
20060631
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
35 b/w illus.
Pages:
352
Dimensions:
5.98x9.01x.78 in. 1.14 lbs.

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Clifford Algebras & Spinors 2ND Edition New Trade Paper
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Product details 352 pages Cambridge University Press - English 9780521005517 Reviews:
"Synopsis" by , This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors.
"Synopsis" by , This is the second edition of Professor Lounesto's introduction to Clifford algebras and spinors.
"Synopsis" by , Here, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. This will interest physicists as well as mathematicians, and includes treatments of the quantum mechanics of the electron, electromagnetism and special relativity with Clifford algebras.
"Synopsis" by , 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.
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