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.
Table of ContentsPreface. Dirac Operators and Clifford Geometry - New Unifying Principles in Particle Physics; Th. Ackermann. On the Hayman Uniqueness Problem for Polyharmonic Functions; M.B. Balk, M.Ya. Mazalov. Left-Linear and Nonlinear Riemann Problems in Clifford Analysis; S. Bernstein. Spin Structures and Harmonic Spinors on Nonhyperelliptic Riemann Surfaces of Small Genera; J. Bures. Decomposition of Analytic Hyperbolically Harmonic Functions; P. Cerejeiras. Spin Gauge Theories: A Summary; J.S.R. Chisholm, R.S. Farwell. Manifolds with and Without Embeddings; J. Cnops. Dirac Equation in the Clifford Algebra of Space; C. Daviau. Dirac Theory from a Field Theoretic Point of View; B. Fauser. On Some Applications of the Biharmonic Equation; K. Gürlebeck. Spinor Particle Mechanics; D. Hestenes. Clifford Analysis and Elliptic Boundary Value Problems in Unbounded Domains; U. Kähler. Twistors and Clifford Algebras; J. Keller. How Many Essentially Different Function Theories Exist? V.V. Kisil. Variational Property of the Peano Kernel for Harmonicity Differences of Order p; W. Haussmann, O.I. Kounchev. Clifford Analysis on the Sphere; P. Van Lancker. Type-Changing Transformations of Pseudo-Euclidean Hurwitz Pairs, Clifford Analysis, and Particle Lifetimes; J. Lawrynowicz. Modified Quaternionic Analysis in R4; Th. Hempfling, H. Leutwiler. Geometric Algebra and Lobachevski Geometry; H. Li. Generalizing the (F,G)-Derivative in the Sense of Bers; H.R. Malonek. Formes quadratiques de Hardy-Weinberg et algèbres de Clifford; A. Micali. On Dirac Equations in Curved Space-Times; D. Miralles. Some Partial Differential Equations in Clifford Analysis; E. Obolashvili. Teaching Clifford Algebra as Physical Mathematics;J.M. Parra. Polydimensional Relativity, a Classical Generalization of the Automorphism Invariance Principle; W.M. Pezzaglia Jr. Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum; W.A. Rodrigues Jr., J. Vaz Jr. Higher Spin and the Spacetime Algebra; S. Somaroo. Curved Radon Transforms in Clifford Analysis; F. Sommen. On a Class of Non-Linear Boundary Value Problems; W. Sprössig. Pin Structures and the Dirac Operator on Real Projective Spaces and Quadrics; M. Cahen, et al. Construction of Monopoles and Instantons by Using Spinors and the Inversion Theorem; J. Vaz Jr. Determinants, Manifolds with Boundary and Dirac Operators; K.P. Wojciechowski, et al. New Dynamical Equations for Many Particle System on the Basis of Multicomplex Algebra; R. Yamaleev.