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

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.