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.
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.
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.
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.
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