Clifford Algebras and Their Applications in Mathematical Physics: Proceedings of the Third Conference Held at Deinze, Belgium, 1993

ISBN-13: 9789401048866 / Angielski / Miękka / 2014 / 411 str.

F. Brackx; Sylvia Delanghe; H. Serras

Opis

This International Conference on Clifford AlgebrfU and Their Application, in Math- ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com- mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.

Spis treści

CLIFFORD ALGEBRAS and APPLICATIONS.- Quantum Clifford algebras.- Relations between Witt rings and Brauer groups.- Clifford algebra tables.- Finite geometry and the table of real Clifford algebras.- Jordan form in Clifford algebra.- CLIFFORD ANALYSIS: Local and global theory for Dirac—type operators.- Elliptic boundary value problems in unbounded domains.- Dirac operators and manifolds with boundary.- Spin structures and harmonic spinors on Riemann surfaces.- Spherical geometry and Möbius transformations.- Cauchy transforms and bi—axial monogenic power functions.- Note on the use of spherical vectorfields in Clifford analysis.- Quaternionic analysis and transmission problems.- C*—algebras of nonlocal quaternionic convolution type operators.- On the solutions of $$ {D^N}{\text{ }}{\hat D^M}{\text{ }}F = 0$$.- Biregular quaternionic functions.- Monogenic and holomorphic functions.- Hypercomplex differentiability and its applications.- Clifford algebras and boundary estimates for harmonic functions.- Regularity of functions with values in Clifford algebra based on a generalized axially symmetric potential theory operator.- On the analogue of the $$ \bar \partial$$ —problem in quaternionic analysis.- Hurwitz pairs and Clifford algebra representations.- On the Bergmann kernel function in the Clifford analysis.- SO(M)—invariant operators on Clifford tensors.- Invariant differential operators on polynomial—valued functions.- A distributional approach to vector manifolds.- Clifford analysis for higher spins.- Quaternionic operator calculus and domain perturbation problems.- Classical Mechanics.- A hamiltonian model of dissipation with Clifford algebraic generalizations.- A formulation of hamiltonian mechanics using geometric calculus.- Mathematical Physics.- Local automorphism invariance: a generalization of general relativity.- Differential forms in geometric calculus.- Clifford valued convolution operator algebras on the Heisenberg group.- Classical solutions of the Dirac equation: bound Coulomb states in Aharonov-Bohm and Zeeman fields.- Geometric algebra versus numerical cartesianism.- Classification of multivector theories and the modification of the postulates of physics.- The “ideal” approach to spinors reconsidered.- Geometric aspects of spinors.- A basis for double solution theory.- Spatial inversion and spinors.- Physical Models.- Non abelian gauge fields in the real Clifford algebra of space time.- Spin gauge theories: principles and predictions.- Gravity as a gauge theory in the spacetime algebra.- Cosmological consequences of a flat—space theory of gravity.- Zitterbewegung and electron structure.- Separation of the Dirac equation and positive definiteness of quantum numbers.