**Clifford Algebras and their**
**Applications in Mathematical Physics**
*Set Volumes 1 & 2: Algebra and Physics & Clifford
Analysis*
**Edited by Rafal Ablamowicz, ***Tennessee Technological University,
Cookeville, TN, ***Bertfried**
**Fauser, ***Universität Konstanz, Germany, ***John Ryan,
***University
of Arkansas, Fayetteville, AR* *&*
**Wolfgang Sprößig, ***TU-Bergakademie, Freiberg, Germany*
Leading experts in the rapidly evolving field of Clifford
(geometric) algebras have contributed to this comprehensive two-volume
text.
Consisting of thematically organized chapters, the volume
is a broad overview of cutting-edge topics in mathematical physics and
the
physical applications of Clifford algebras.
Volume I "Algebra and Physics" is devoted to the mathematical
aspects of Clifford algebras and their applications in physics. Algebraic
geometry, cohomology, non-commutative spaces, *q*-deformations
and the related quantum groups, and projective geometry provide the
basis for algebraic topics covered. Physical applications
and extensions of physical theories such as the theory of quaternionic
spin, Dirac
theory of electron, plane waves and wave packets in electrodynamics,
and electron scattering are also presented, showing the broad
applicability of Clifford geometric algebras in solving
physical problems. Treatment of the structure theory of quantum Clifford
algebras,
twistor phase space, introduction of a Kaluza-Klein type
theory related to Finsler geometry, the connection to logic, group representations,
and computational techniques—including symbolic calculations
and theorem proving—round out the presentation.
Volume 2 "Clifford Analysis" is an up-to-date survey of
most aspects of modern-day 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, monogenic and hypermonogenic functions
and their derivatives, Euclidean Beltrami equations, Fourier theory under
Möbius
transformations, and applications to operator theory
and scattering theory.
Thanks to a careful balance of mathematical theory and
applications to physics, the two volumes are accessible to both graduate
students and
specialists in the general area of Clifford algebras
and their applications. |