By Carlos A. Berenstein, Der-Chen Chang, Wayne M. Eby (auth.), Rafał Abłamowicz (eds.)
The invited papers during this quantity offer an in depth exam of Clifford algebras and their value to geometry, research, physics, and engineering. Divided into 5 elements, the book's first part is dedicated to Clifford research; right here, subject matters surround the Morera challenge, inverse scattering linked to the Schrödinger equation, discrete Stokes equations within the aircraft, a symmetric sensible calculus, Poincaré sequence, differential operators in Lipschitz domain names, Paley-Wiener theorems and Shannon sampling, Bergman projections, and quaternionic calculus for a category of boundary worth problems.
A cautious dialogue of geometric functions of Clifford algebras follows, with papers on hyper-Hermitian manifolds, spin buildings and Clifford bundles, differential types on conformal manifolds, connection and torsion, Casimir parts and Bochner identities on Riemannian manifolds, Rarita-Schwinger operators, and the interface among noncommutative geometry and physics. additionally, cognizance is paid to the algebraic and Lie-theoretic purposes of Clifford algebras---particularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and linked mathematical constructions. Symplectic Clifford algebras also are discussed.
Finally, Clifford algebras play a robust function in either physics and engineering. The physics part positive aspects an research of geometric algebras, chiral Dirac equations, spinors and Fermions, and purposes of Clifford algebras in classical mechanics and common relativity. Twistor and octonionic tools, electromagnetism and gravity, simple particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the normal version are between issues thought of at size. The part dedicated to engineering purposes contains papers on twist representations for cycloidal curves, an outline of a picture area utilizing Cayley-Klein geometry, pose estimation, and implementations of Clifford algebra co-processor design.
While the papers accrued during this quantity require that the reader own an effective wisdom of applicable heritage fabric, they result in the most up-tp-date examine issues. With its wide variety of themes, well-established members, and perfect references and index, this e-book will entice graduate scholars and researchers.
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