Titlebook: Clifford Algebras and Their Applications in Mathematical Physics; J. S. R. Chisholm,A. K. Common Book 1986 D. Reidel Publishing Company, D

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The Biregular Functions of Clifford Analysis: Some Special Topicsmorphy of complex analysis. We will make it clear that multi-valued functions cannot be avoided in this study. Some examples of domains of biregula- rity will be given, by constructing biregular functions in the domains which cannot be extended to any larger domain.

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Clifford Algebras and Spinorsclidean spaces over reals have a natural linear structure over reals, complex numbers or quaternions. Clifford algebras have involutions which induce bilinear forms or scalar products on spinor spaces. The automorphism groups of these scalar products of spinors are determined and also classified.

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A New Representation for Spinors in Real Clifford Algebrasm” for Dirac spinors introduced by D. Hestenes. The spinor spaces obtained thus are related to a Clifford subalgebra of the parent algebra. Classification of real Clifford algebras and interior products of spinors together with their isometry groups are discussed.

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Spin Groups Associated with Degenerate Orthogonal Spacesparticularly to forms with nullspace of dimensions one and two, and explicit computations illustrate the connection to representations of inhomogeneous orthogonal groups of interest in physics. This provides a unified picture of relativistic and non-relativistic covariant wave equations for spinning

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Spingroups and Spherical MonogenicsSpin(m). This leads to the spherical monogenics as a refinement of the spherical harmonics. We also develop a scheme to construct solutions to partial differential equations with constant coefficients which are Spin(m)-invariant.