This edited volume consists of 20 contributions showing applications of Clifford algebras in quantum mechanics, field theory, spinor calculus, projective geometry, hypercomplex algebra, function theory, crystallography, and in classroom teaching of mathematical physics. They include computations performed with a variety of computer programs such as CLICAL, MAPLE, MATHEMATICA, MATLAB, REDUCE, and computer languages such as FORTRAN and C++. In many instances, computer was used as a tool to derive new results, and, by means of counter-examples, to falsify statements found in literature. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.
Features:
Preface, which introduces the Reader to scientific computing in Clifford algebras and which briefly summarizes each contribution.
Chapters, thematically organized, and carefully edited, which provide a critical survey of Clifford algebras' interactions between computational applications and theory.
Original programs and computer code created by the contributors, which will allow the Reader to experiment, to repeat computations, and to verify results presented by their authors. The software, mostly based on major computer software programs such as CLICAL, MAPLE, MATHEMATICA, and REDUCE, will be available by FTP from the Birkhauser Web Site: http://www.birkhauser.com/books/ISBN/0-8176-397-1.
Numeric computations with FORTRAN, MATLAB and C++ are also considered.
Index, which provides a quick reference to all contributions.
This new book is an excellent resource for those mathematicians, physicists, engineers and scientific computing researchers who currently use Clifford algebra methods in their investigations. It is also appealing to those who would like to quickly become familiar with the theory and computational practice in some of the most recent and fascinating applications of Clifford algebras.
Contents:
Preface * Part 1. Verifying and Falsifying Conjectures: Counterexamples in Clifford Algebras with CLICAL * Part 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 * A Clifford algebra approach to spinor calculus * Computer algebra in spinor calculations * Vahlen matrices for non-definite metrics * Part 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 * Part 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 * Index.
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