Overview

This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry.

Full Product Details

Author:   Rafal Ablamowicz ,  P. Lounesto
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1995
Volume:   321
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.682kg
ISBN:  

9789048145256

ISBN 10:   9048145252
Pages:   425
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Table of Contents/Table des Matières.- Historical Survey.- Some Clifford algebra history.- Clifford Algebras.- Tensors and Clifford algebra.- Sur les algèbres de Clifford III.- Finite geometry, Dirac groups and the table of real Clifford algebras.- Clifford algebra techniques in linear algebra.- Crumeyrolle/Chevalley, Weyl, Pure and Majorana Spinors.- Construction of spinors via Witt decomposition and primitive idempotents: a review.- Crumeyrolle-Chevalley-Riesz spinors and covariance.- Twistors as geometric objects in spacetime.- Crumeyrolle’s bivectors and spinors.- On the relationships between the Dirac spinors and Clifford subalgebra Cl1,3+.- Spinor fields and superfields as equivalence classes of exterior algebra fields.- Chevalley-Crumeyrolle spinors in McKane-Parisi-Sourlas theorem.- Spinors from a differential geometric point of view.- Dirac Operator, Maxwell’s Equations, and Conformal Covariance.- Eigenvalues of the Dirac operator, twistors and Killing spinors on Riemannian manifolds.- Dirac’s field operator ?.- Biquaternionic formulation of Maxwell’s equations and their solutions.- The massless Dirac equation, Maxwell’s equation, and the application of Clifford algebras.- The conformal covariance of Huygens’ principle-type integral formulae in Clifford analysis.- Clifford Analysis, Boundary Value Problems, Hermite Interpolants, and Padé Approximants.- Cliffor-valued functions in Cl3.- Clifford analysis and elliptic boundary value problems.- A complete boundary collocation system.- On the algebraic foundations of the vector ?-algorithm.- Clifford Algebras and Generalizations.- Classical spinor structures on quantum spaces.- A unified metric.- Quantum braided Clifford algebras.- Clifford algebra for Hecke braid.

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