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626 pp., Hardcover , PMP, v.34, 2004

Abstract:

Editor's statement as a direct quote: "Clifford algebras play a strong role in both physics and engineering. The physics section features an investigation of geometric algebras, chiral Dirac equations, spinors and Fermions, and applications of Clifford algebras in classical mechanics and general relativity. Twistor and octonionic methods, electromagnetism and gravity, elementary particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the Standard Model are among topics considered at length. The section devoted to engineering applications includes papers on twist representations for cycloidal curves, a description of an image space using Cayley--Klein geometry, pose estimation, and implementations of Clifford algebra co-processor design." From the book's Contents table: "PART I. CLIFFORD ANALYSIS 1. The Morera Problem in Clifford Algebras and the Heisenberg Group Carlos A. Berenstein, Der-Chen Chang, and Wayne M. Eby 2. Multidimensional Inverse Scattering Associated with the Schrodinger Equation Swanhild Bernstein 3. On Discrete Stokes and Navier--Stokes Equations in the Plane Klaus Garlebeck and Angela Hommel 4. A Symmetric Functional Calculus for Systems of Operators of Type II;Brian Jefferies 5. Poincare' Series in Clifford Analysis Rolf Saren Krausshar 6. Harmonic Analysis for General First Order Differential Operators in Lipschitz Domains Emilio Marmolejo-Olea and Marius Mitrea 7. Paley: Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting Tao Qian 8. Bergman Projection in Clifford Analysis Guangbin Ren and Helmuth R. Malonek 9. Quaternionic Calculus for a Class of Initial Boundary Value Problems Wolfgang Sprassig PART II. GEOMETRY 10. A Nahm Transform for Instantons over ALE Spaces Claudio Bartocci and Marcos Jardim 11. Hyper-Hermitian Manifolds and Connections with Skew-Symmetric Torsion Gueo Grantcharov 12. Casimir Elements and Bochner Identities on Riemannian Manifolds Yasushi Homma 13. Eigenvalues of Dirac and Rarita--Schwinger Operators Doojin Hong 14. Differential Forms Canonically Associated to Even-Dimensional Compact Conformal Manifolds William J. Ugalde 15. The Interface of Noncommutative Geometry and Physics Joseph C. Varilly PART III. MATHEMATICAL STRUCTURES 16. The Method of Virtual Variables and Representations of Lie Superalgebras Andrea Brini, Francesco Regonati, and Antonio Teolis 17. Algebras Like Clifford Algebras Michael Eastwood 18. Grade Free Product FormulaeÃÂæ from Grassmann--Hopf Gebras Bertfried Fauser 19. The Clifford Algebra in the Theory of Algebras, Quadratic Forms, and Classical Groups Alexander Hahn 20. Lipschitz's Methods of 1886 Applied to Symplectic Clifford Algebras Jacques Helmstetter 21. The Group of Classes of Involutions of Graded Central Simple Algebras Jacques Helmstetter 22. A Binary Index Notation for Clifford Algebras Dennis W. Marks 23. Transposition in Clifford Algebra: SU(3) from Reorientation Invariance Bernd Schmeikal PART IV. PHYSICS 24. The Quantum/Classical Interface: Insights from Clifford's (Geometric) Algebra William E. Baylis 25. Standard Quantum Spheres Francesco Bonechi, Nicola Ciccoli, and Marco Tarlini 26. Clifford Algebras, Pure Spinors and the Physics of Fermions Paolo Budinich 27. Spinor Formulations for Gravitational Energy-Momentum Chiang-Mei Chen, James M. Nester, and Roh-Suan Tung 28. Chiral Dirac Equations Claude Daviau 29. Using Octonions to Describe Fundamental Particles Tevian Dray and Corinne A. Manogue 30. Applications of Geometric Algebra in Electromagnetism, Quantum Theory and Gravity Anthony Lasenby, Chris Doran, and Elsa Arcaute 31. Noncommutative Physics on Lie Algebras, ( 2)n Lattices and Clifford Algebras Shahn Majid 32. Dirac Operator on Quantum Homogeneous Spaces and Noncommutative Geometry Robert M. Owczarek 33. r-Fold Multivectors and Superenergy Jose M. Pozo and Josep M. Parra: An Approach to the Standard Model Greg Trayling and William E. Baylis PART V. APPLICATIONS IN ENGINEERING 35. Implementation of a Clifford Algebra Co-Processor Design on a Field Programmable Gate Array Christian Perwass, Christian Gebken, and Gerald Sommer 36. Image Space Jan J. Koenderink 37. Pose Estimation of Cycloidal Curves by using Twist Representations Bodo Rosenhahn and Gerald Sommer. + INDEX."

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Copyright@2004 by Birkhauser http://math.tntech.edu/rafal/cookeville/proceedings/InvitedForm.pdf

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