The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. 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.
Inhaltsverzeichnis
I. Clifford Analysis. - 1. The Morera Problem in Clifford Algebras and the Heisenberg Group. - 2. Multidimensional Inverse Scattering Associated with the Schrödinger Equation. - 3. On Discrete Stokes and Navier Stokes Equations in the Plane. - 4. A Symmetric Functional Calculus for Systems of Operators of Type ? . - 5. Poincaré Series in Clifford Analysis. - 6. Harmonic Analysis for General First Order Differential Operators in Lipschitz Domains. - 7. Paley Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting. - 8. Bergman Projection in Clifford Analysis. - 9. Quaternionic Calculus for a Class of Initial Boundary Value Problems. - II. Geometry. - 10. A Nahm Transform for Instantons over ALE Spaces. - 11. Hyper-Hermitian Manifolds and Connections with Skew-Symmetric Torsion. - 12. Casimir Elements and Bochner Identities on Riemannian Manifolds. - 13. Eigenvalues of Dirac and Rarita Schwinger Operators. - 14. Differential Forms Canonically Associated to Even-Dimensional Compact Conformal Manifolds. - 15. The Interface of Noncommutative Geometry and Physics. - III. Mathematical Structures. - 16. The Method of Virtual Variables and Representations of Lie Superalgebras. - 17. Algebras Like Clifford Algebras. - 18. Grade Free Product Formulæ from Grassmann Hopf Gebras. - 19. The Clifford Algebra in the Theory of Algebras, Quadratic Forms, and Classical Groups. - 20. Lipschitz s Methods of 1886 Applied to Symplectic Clifford Algebras. - 21. The Group of Classes of Involutions of Graded Central Simple Algebras. - 22. A Binary Index Notation for Clifford Algebras. - 23. Transposition in Clifford Algebra: SU(3) from Reorientation Invariance. - IV. Physics. - 24. The Quantum/Classical Interface: Insights from Clifford s (Geometric) Algebra. - 25. Standard Quantum Spheres. - 26. Clifford Algebras, Pure Spinors and the Physics of Fermions. - 27. Spinor Formulations for Gravitational Energy-Momentum. - 28. Chiral Dirac Equations. - 29. Using Octonions to Describe Fundamental Particles. - 30. Applications of Geometric Algebra in Electromagnetism, Quantum Theory and Gravity. - 31. Noncommutative Physics on Lie Algebras, (? 2)n Lattices and Clifford Algebras. - 32. Dirac Operator on Quantum Homogeneous Spaces and Noncommutative Geometry. - 33. r-Fold Multivectors and Superenergy. - 34. The Cl7 Approach to the Standard Model. - V. Applications in Engineering. - 35. Implementation of a Clifford Algebra Co-Processor Design on a Field Programmable Gate Array. - 36. Image Space. - 37. Pose Estimation of Cycloidal Curves by using Twist Representations.
