By Carlos A. Berenstein, Der-Chen Chang, Wayne M. Eby (auth.), Rafał Abłamowicz (eds.)

The invited papers during this quantity supply an in depth exam of Clifford algebras and their importance to geometry, research, physics, and engineering. Divided into 5 elements, the book's first part is dedicated to Clifford research; right here, issues surround the Morera challenge, inverse scattering linked to the Schrödinger equation, discrete Stokes equations within the airplane, a symmetric useful 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 price 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 components and Bochner identities on Riemannian manifolds, Rarita-Schwinger operators, and the interface among noncommutative geometry and physics. furthermore, consciousness 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 buildings. Symplectic Clifford algebras also are discussed.

Finally, Clifford algebras play a powerful position in either physics and engineering. The physics part good points an research of geometric algebras, chiral Dirac equations, spinors and Fermions, and functions of Clifford algebras in classical mechanics and basic relativity. Twistor and octonionic equipment, electromagnetism and gravity, user-friendly particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the traditional version are between issues thought of at size. The part dedicated to engineering functions 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 acceptable historical past fabric, they bring about the most up-tp-date study themes. With its wide variety of themes, well-established participants, and perfect references and index, this booklet will entice graduate scholars and researchers.