Clifford Algebras Applications to Mathematics, Physics, and Engineering
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 t...
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| Format: | eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser
2004, 2004
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| Edition: | 1st ed. 2004 |
| Series: | Progress in Mathematical Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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