Clifford Algebras and Their Applications in Mathematical Physics

1 Partial Differential Equations and Boundary Value Problems.- On Quaternionic Beltrami Equations.- The M¿bius Transformation, Green Function and the Degenerate Elliptic Equation.- Quaternionic Analysis in Fluid Mechanics.- 2 singular Integral Operators.- Fourier Theory Under M¿bius Transformations.- On the Cauchy Type Integral and the Riemann Problem.- Convolution and Maximal Operator Inequalities in Clifford Analysis.- 3 Applications in Geometry and Physics.- A Borel-Pompeiu Formula in ?n and Its Application to Inverse Scattering Theory.- Complex-Distance Potential Theory and Hyperbolic Equations.- Specific Representations for Members of the Holonomy Group.- An Extension of Clifford Analysis Towards Super-symmetry.- The Geometry of Generalized Dirac Operators and the Standard Model of Particle Physics.- 4 M¿bius Transformations and Monogenic Functions.- The Schwarzian and M¿bius Transformarions in Higher Dimensions.- The Structure of Monogenic Functions.- On the Radial Part of the Cauchy-Riemann Operator.- Hypercomplex Derivability ¿ The Characterization of Monogenic Functions in ?n+1 by Their Derivative.- Hypermonogenic Functions.- Reproducing Kernels for Hyperbolic Spaces.

The second part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. This volume is a survey of most aspects of Clifford analysis. Topics range from applications such as complex-distance potential theory, supersymmetry, and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications, to mathematical physics and Schwarzian derivatives in Euclidean space. Among the mathematical topics examined are generalized Dirac operators, holonomy groups, monogenic and hypermonogenic functions and their derivatives, quaternionic Beltrami equations, Fourier theory under Mobius transformations, Cauchy-Reimann operators, and Cauchy type integrals.