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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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书目名称Clifford Algebras and Their Applications in Mathematical Physics
编辑J. S. R. Chisholm,A. K. Common
视频video
丛书名称Nato Science Series C:
图书封面Titlebook: Clifford Algebras and Their Applications in Mathematical Physics;  J. S. R. Chisholm,A. K. Common Book 1986 D. Reidel Publishing Company, D
描述William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann‘s algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs­ Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley‘s book, ‘The Algebraic Theory
出版日期Book 1986
关键词algebra; calculus; differential equation; gauge theory; mathematical physics; minimum
版次1
doihttps://doi.org/10.1007/978-94-009-4728-3
isbn_softcover978-94-010-8602-8
isbn_ebook978-94-009-4728-3Series ISSN 1389-2185
issn_series 1389-2185
copyrightD. Reidel Publishing Company, Dordrecht, Holland 1986
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Primitive Idempotents and Indecomposable Left Ideals in Degenerate Clifford Algebrasmposition of A into a direct sum of principal indecomposable modules can be lifted to a corresponding decomposition of A. The resulting indecomposable summands of A need not be minimal. As an example, principal indecomposable modules of degenerate Clifford algebras with degeneracy in one dimension are found.
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Generalized C-R Equations on Manifoldss generalizations of C-R equations, studied by different authors during last 50 years, are discussed and it is shown how they fit into the scheme. A special attention is paid to the most interesting case of dimension 4 and to the connection of the described systems of equations with equations in mathematical physics.
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Integral Formulae in Complex Clifford Analysissis e.g.Riesz’ integral formula for the solution of the wave equation in the Minkowski space and Penrose’s integral formula for a spin-1/2 massless field. There are good hopes that the new integral formula of hyperbolic type can be used to give further information on left regular mappings and spinor fields.
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Responsibility in Nanotechnology Developmentsis e.g.Riesz’ integral formula for the solution of the wave equation in the Minkowski space and Penrose’s integral formula for a spin-1/2 massless field. There are good hopes that the new integral formula of hyperbolic type can be used to give further information on left regular mappings and spinor fields.
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Pseudo-Euclidean Hurwitz Pairs and Generalized Fueter Equationsrch is connected with an analogue of the quoted construction if the vector spaces V and S in question are equipped with . with standard properties. This enables the authors to introduce and study some ., extending or improving certain results on holomorphy due to F. Brackx, R. Delanghe, V. Souček, A. Vaz Ferreira, and others.
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