Rafal Ablamowicz (Hrsg.)

Clifford Algebras

Applications to Mathematics, Physics, and Engineering
Herausgegeben:Ablamowicz, Rafal

• Gebundenes Buch

Produktbeschreibung

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to geometry, analysis, physics, and engineering. Divided into five parts, the book's first section is devoted to Clifford analysis; here, topics encompass the Morera problem, inverse scattering associated with the Schrödinger equation, discrete Stokes equations in the plane, a symmetric functional calculus, Poincaré series, differential operators in Lipschitz domains, Paley-Wiener theorems and Shannon sampling, Bergman projections, and quaternionic calculus for a class of boundary value problems.

A careful discussion of geometric applications of Clifford algebras follows, with papers on hyper-Hermitian manifolds, spin structures and Clifford bundles, differential forms on conformal manifolds, connection and torsion, Casimir elements and Bochner identities on Riemannian manifolds, Rarita-Schwinger operators, and the interface between noncommutative geometry and physics. In addition, attention is paid to the algebraic and Lie-theoretic applications of Clifford algebras---particularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and associated mathematical structures. Symplectic Clifford algebras are also discussed.

Finally, 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, andimplementations of Clifford algebra co-processor design.

While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

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Produktdetails

• Progress in Mathematical Physics 34
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 978-0-8176-3525-1
• 2004
• Seitenzahl: 626
• Erscheinungstermin: 4. Dezember 2003
• Englisch
• Abmessung: 245mm x 162mm x 34mm
• Gewicht: 1040g
• ISBN-13: 9780817635251
• ISBN-10: 0817635254
• Artikelnr.: 12586201

Inhaltsangabe

PREFACE PART I. CLIFFORD ANALYSIS 1. The Morera Problem in Clifford Algebras and the Heisenberg Group by Carlos A. Berenstein, Der-Chen Chang, and Wayne M. Eby 2. Multidimensional Inverse Scattering Associated with the Schrödinger Equation by Swanhild Bernstein 3. On Discrete Stokes and Navier Stokes Equations in the Plane by Klaus Gürlebeck and Angela Hommel 4. A Symmetric Functional Calculus for Systems of Operators of Type w by Brian Jefferies 5. Poincaré Series in Clifford Analysis by Rolf Sören Krausshar 6. Harmonic Analysis for General First Order Differential Operators in Lipschitz Domains by Emilio Marmolejo-Olea and Marius Mitrea 7. Paley Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting by Tao Qian 8. Bergman Projection in Clifford Analysis by Guangbin Ren and Helmuth R. Malonek 9. Quaternionic Calculus for a Class of Initial Boundary Value Problems by Wolfgang Sprössig PART II. GEOMETRY 10. A Nahm Transform for Instantons over ALE Spaces by Claudio Bartocci and Marcos Jardim 11. Hyper-Hermitian Manifolds and Connections with Skew-Symmetric Torsion by Gueo Grantcharov 12. Casimir Elements and Bochner Identities on Riemannian Manifolds by Yasushi Homma 13. Eigenvalues of Dirac and Rarita Schwinger Operators by Doojin Hong 14. Differential Forms Canonically Associated to Even-Dimensional Compact Conformal Manifolds by William J. Ugalde 15. The Interface of Noncommutative Geometry and Physics by Joseph C. Várilly PART III. MATHEMATICAL STRUCTURES 16. The Method of Virtual Variables and Representations of Lie Superalgebras by Andrea Brini, Francesco Regonati, and Antonio Teolis 17. Algebras Like Clifford Algebras by Michael Eastwood 18. Grade Free Product Formulæ from Grassmann Hopf Gebras by Bertfried Fauser 19. The Clifford Algebra in the Theory of Algebras, Quadratic Forms, and Classical Groups by Alexander Hahn 20. Lipschitz s Methods of 1886 Applied to SymplecticClifford Algebras by Jacques Helmstetter 21. The Group of Classes of Involutions of Graded Central Simple Algebras by Jacques Helmstetter 22. A Binary Index Notation for Clifford Algebras by Dennis W. Marks 23. Transposition in Clifford Algebra: SU(3) from Reorientation Invariance by Bernd Schmeikal PART IV. PHYSICS 24. The Quantum/Classical Interface: Insights from Clifford s (Geometric) Algebra by William E. Baylis 25. Standard Quantum Spheres by Francesco Bonechi, Nicola Ciccoli, and Marco Tarlini 26. Clifford Algebras, Pure Spinors and the Physics of Fermions by Paolo Budinich 27. Spinor Formulations for Gravitational Energy-Momentum by Chiang-Mei Chen, James M. Nester, and Roh-Suan Tung 28. Chiral Dirac Equations by Claude Daviau 29. Using Octonions to Describe Fundamental Particles by Tevian Dray and Corinne A. Manogue 30. Applications of Geometric Algebra in Electromagnetism, Quantum Theory and Gravity by Anthony Lasenby, Chris Doran, and Elsa Arcaute 31. Noncommutative Physics on Lie Algebras, (Z2)n Lattices and Clifford Algebras by Shahn Majid 32. Dirac Operator on Quantum Homogeneous Spaces and Noncommutative Geometry by Robert M. Owczarek 33. r-Fold Multivectors and Superenergy by Jose M. Pozo and Josep M. Parra 34. The Cl7 Approach to the Standard Model by 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 by Christian Perwass, Christian Gebken, and Gerald Sommer 36. Image Space by Jan J. Koenderink 37. Pose Estimation of Cycloidal Curves by using Twist Representations by Bodo Rosenhahn and Gerald Sommer INDEX