Clifford Algebras and Their Applications in Mathematical Physics

ISBN-13: 9780792316237 / Angielski / Twarda / 1992 / 526 str.

Artibano Micali; A. Micali; R. Boudet

Opis

This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example, gauge fields, relativity theory, supersymmetry and supergravity, and condensed phase physics. Included is a biography and list of publications of Mario Schenberg, who, next to Marcel Riesz, has made valuable contributions to these topics.
This volume will be of interest to mathematicians working in the fields of algebra, geometry or special functions, to physicists working on quantum mechanics or supersymmetry, and to historians of mathematical physics.

Spis treści

General Survey.- Mathematical Viruses.- Clifford Algebras and Related Topics.- Algebraic spinors for R9,1.- Tetrahedral structure of idempotents of the Clifford algebra C3,1.- Clifford groups for arbitrary quadratic forms.- Clifford algebra calculations with a microcomputer.- Clifford algebras and Möbius transformations.- Algèbres de Clifford sur un Corps de Caractéristique 2.- Real projective representations of real Clifford algebras and reflection groups.- Parallel treatment of Riemannian and Symplectic Clifford algebras.- Classification, properties and applications of the Majorana representations of the real Clifford algebras Cp, q.- On the classification of Clifford algebras as quadratic spaces in the case where the dimension is infinite and the base field has characteristic 2.- On the kernel and image of the spin representation.- Finite geometries and Clifford algebras III.- Generalized Clifford algebras and their representations.- Algebraic spin structures.- Clifford algebras and torogonal structures.- The idempotent structure of an infinite dimensional Clifford algebra.- On spinor classifications.- Clifford Analysis.- HP spaces of monogenic functions.- Twistor correspondence in higher even dimensions.- A Gram-Schmidt method in Hilbert modules.- The relative position of L2 domains in Clifford Analysis.- A note on generalized Rademacher and hyperbolic functions.- Fueter-Hurwitz Regular mappings and an integral representation.- Spin-gauge unification of integrable non linear systems.- On the linearization of a partial differential operator and p-hyperholomorphic functions.- Algebres de Clifford-Hilbert et operateurs de Vertex.- Singular integral operators in Clifford Analysis.- Simplicial calculus with Geometric Algebra.- Clifford Analysis and Integral Geometry.- Fundamental solutions for operators which are polynomials in the Dirac operator.- On eigenvalue estimates of nonlinear Stokes eigenvalue problems.- Mathematical Physics.- Gauge field equation on principal fibre bundle. A Clifford Algebra formulation.- Les Algebres de Clifford et les transformations des multivecteurs. L’Algebre de Clifford de R(1,3) et la constante de Planck.- Theorie relativiste du nucleon et du doublet ?.- Unified spin gauge theories of the four fundamental forces.- The geometric structure of the space of fermionic physical observables.- Supergravity, supersymmetry: a geometric unitary spinor theory.- Fermions as special states of bosons.- Harmonic coordinates and the electromagnetic field.- Clifford Analysis and systems of condensed phase.- The multivector structure of the matter and interaction field theories.- The normed maps ?11 × ?11 ? ?26 in Hypercomplex Analysis and in Physics.- On Dirac and Dirac-Darwin-Hestenes Equations.- Geometrical content of the Fierz identities.- Historical Aspects of Clifford Algebras.- Notice biographique sur Màrio Schenberg.- Algebraic Structures of Finite Point Sets I.