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Showing 1 to 12 of 12 for “"clifford algebra"”.
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Pointwise and uniform convergence of fourier series on SU(2)
… on SU (2), due to Liu and Qian, were obtained by Clifford algebra techniques. We obtain similar versions of these theorems using simpler proof techniques: classical harmonic analysis and group theory"--Abstract, page iii.</p>
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The Fock-Schwartz spin representation space
… as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the Dirac-Ramond operator on the loop space of a string manifold.
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A space-time approach to quantum mechanics
… development and application of Geometric Algebra, an extended vector calculus. The entire algebraic structure, which is a graded Clifford algebra, is developed. To illustrate the derived results, examples are given for two and three dimensions. Here it becomes clear, how rotations and …
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On the structure of geometries with spinor-type connexion
… a synthesis, using standard techniques of algebra and of differential geometry, of some of the principal ideas and structures of the classical fieldtheoretic description of spinor fields in curved space-time. A geometric model for spinor fields in curved space-time is described which is …
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Geometry, Kinematics, and Rigid Body Mechanics in Cayley-Klein Geometries
… Grundlagen aus projektiver Geometrie, äußerer Algebra und quadratischen Formen vorgestellt, um darauf aufbauend eine Klasse von Cayley-Klein Räumen zu beschreiben. Diese Klasse enthält die drei klassischen Räume konstanter Krümmung (euklidisch, elliptisch und hyperbolisch). Die entsprechenden …
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New relativistic solutions for classical charges in an electromagnetic field.
… Lorentz transformations in the framework of the Clifford algebra Cℓ3. The paravector subspace of the algebra, a four-dimensional space defined to contain scalars and spatial vectors, shares the metric structure of Minkowski spacetime. With the flexible advantage of Clifford algebras in vector …
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Multidimensional distributions and generalized Hilbert transforms in Clifford analysis
… of the Hilbert transform in the framework of Clifford analysis. Clifford analysis is a higher dimensional function theory in the framework of a Clifford algebra which may be seen as a multidimensional generalization of the theory of holomorphic functions in one complex variable and – at the …
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A study of vertex operator constructions for some infinite dimensional lie algebras
… we construct a module for the toroidal Lie algebra and the extended toroidal Lie algebra of type A₁. The Fock module representation obtained here is faithful and completely reducible over the extended toroidal Lie algebra. We also study the level two vertex operator representation of the …
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Formalizing Clifford algebras and related constructions in the Lean theorem prover
Geometric Algebra (GA) is a mathematical framework used primarily by engineers and physicists, while theorem proving software has its background originally in computer science departments. This thesis brings the former into the language of the latter, in the more abstract setting of Clifford …
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Relativistische Quantendynamik in extrem starken Laserfeldern
… durchgängig den Formalismus der sogenannten Clifford-Algebra über dem 3+1-dimensionalen Minkowski-Raum, die auch als reelle Dirac- oder Raumzeit-Algebra bezeichnet wird. Die erstellten Programme basieren daher auf einer Implementierung dieser Algebra in Form einer C++-Bibliothek. Der …
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Applications of Geometric Algebra in Mathematical Engineering
Geometric Algebra (GA) has found success in various areas of the physical sciences and engineering over the last decade but remains relatively underutilised in industry and several key topics in the field remain unexplored. This thesis focuses on the practical applications of Geometric Algebra in …
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Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
… complex) noncommutative and nonassociative algebras $\bbO_{p,q}$ (resp. $\bbO_{n}$) generalizing the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras. Introduced by Morier-Genoud and Ovsienko, these …