Clifford Algebras and Their Application in Mathematical Physics

1. Front Matter

   Pages i-xxxii

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2. Dirac Operators and Clifford Geometry — New Unifying Principles in Particle Physics?

   • Thomas Ackermann

   Pages 1-10

3. On the Hayman Uniqueness Problem for Polyharmonic Functions

   • M. B. Balk, M. Ya. Mazalov

   Pages 11-16

4. Left-Linear and Nonlinear Riemann Problems in Clifford Analysis

   • Swanhild Bernstein

   Pages 17-30

5. Spin Structures and Harmonic Spinors on Nonhyperelliptic Riemann Surfaces of Small Genera

   • Jarolím Bureš

   Pages 31-43

6. Decomposition of Analytic Hyperbolically Harmonic Functions

   • P. Cerejeiras

   Pages 45-51

7. Spin Gauge Theories: A Summary

   • J. S. R. Chisholm, R. S. Farwell

   Pages 53-56

8. Manifolds with and without Embeddings

   • J. Cnops

   Pages 57-65

9. Dirac Equation in the Clifford Algebra of Space

   • Claude Daviau

   Pages 67-87

10. Dirac Theory from a Field Theoretic Point of View

    • Bertfried Fauser

    Pages 89-107

11. On Some Applications of the Biharmonic Equation

    • K. Gürlebeck

    Pages 109-128

12. Spinor Particle Mechanics

    • David Hestenes

    Pages 129-143

13. Clifford Analysis and Elliptic Boundary Value Problems in Unbounded Domains

    • Uwe Kähler

    Pages 145-160

14. Twistors and Clifford Algebras

    • Jaime Keller

    Pages 161-173

15. How Many Essentialy Different Function Theories Exist?

    • Vladimir V. Kisil

    Pages 175-184

16. Variational Property of the Peano Kernel for Harmonicity Differences of Order p

    • Werner Haussmann, Ognyan I. Kounchev

    Pages 185-199

17. Clifford Analysis on the Sphere

    • P. Van Lancker

    Pages 201-215

18. Type-Changing Transformations of Pseudo-Euclidean Hurwitz Pairs, Clifford Analysis, and Particle Lifetimes

    • Julian Lawrynowicz

    Pages 217-226

19. Modified Quaternionic Analysis in ℝ ⁴

    • Thomas Hempfling, Heinz Leutwiler

    Pages 227-237

20. Geometric Algebra and Lobachevski Geometry

    • Li Hongbo

    Pages 239-245

Clifford Algebras continues to be a fast-growing discipline, with ever-increasing applications in many scientific fields. This volume contains the lectures given at the Fourth Conference on Clifford Algebras and their Applications in Mathematical Physics, held at RWTH Aachen in May 1996. The papers represent an excellent survey of the newest developments around Clifford Analysis and its applications to theoretical physics.
Audience: This book should appeal to physicists and mathematicians working in areas involving functions of complex variables, associative rings and algebras, integral transforms, operational calculus, partial differential equations, and the mathematics of physics.

• Boundary value problem
• Riemann surfaces
• algebra
• electromagnetic wave
• integral transform
• partial differential equation
• partial differential equations

• Department of Mathematics, Rheinisch-Westfälischen Technischen Hochschule, Aachen, Germany

  Volker Dietrich, Klaus Habetha, Gerhard Jank

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