Clifford Algebras with Numeric and Symbolic Computations

ISBN-13: 9781461581598 / Angielski / Miękka / 2012 / 340 str.

Rafal Ablamowicz; Joseph Parra; Pertti Lounesto

Opis

This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail.

Recenzje

"Presents for the first time a comprehensive overview of the interaction between Clifford algebras and mathematical computations... Provides an excellent source of reference for researchers, educators and students...who seek for advanced computing tools and those working on the design and implementation of algorithms."

--The Sac Newsletter

Spis treści

1. Verifying and Falsifying Conjectures.- Counterexamples in Clifford algebras with CLICAL.- 2. Differential Geometry, Quantum Mechanics, Spinors and Conformal Group.- The use of computer algebra and Clifford algebra in teaching mathematical physics.- General Clifford algebra and related differential geometry calculations with MATHEMATICA.- Pauli-algebra calculations in MAPLE V.- The generative process of space-time and strong interaction quantum numbers of orientation.- On a new basis for a generalized Clifford algebra and its application to quantum mechanics.- Vector continued fraction algorithms.- LUCY: A Clifford algebra approach to spinor calculus.- Computer algebra in spinor calculations.- Vahlen matrices for non-definite metrics.- 3. Generalized Clifford Algebras and Number Systems, Projective Geometry and Crystallography.- On Clifford algebras of a bilinear form with an antisymmetric part.- A unipodal algebra package for MATHEMATICA.- Octonion X-product orbits.- A commutative hypercomplex algebra with associated function theory.- On generalized Clifford algebras — recent applications.- Oriented projective geometry with Clifford algebra.- The applications of Clifford algebras to crystallography using MATHEMATICA.- 4. Numerical Methods in Clifford Algebras.- Orthonormal basis sets in Clifford algebras.- Complex conjugation — relative to what?.- Object-oriented implementations of Clifford algebras in C++: a prototype.