Clifford Algebras and Their Applications in Mathematical Physics

Paperback (Softcover reprint of the original 1st ed. 1986)
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More About This Book

Product Details

  • ISBN-13: 9789401086028
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2013
  • Series: Nato Science Series C: (closed) , #183
  • Edition description: Softcover reprint of the original 1st ed. 1986
  • Pages: 616
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.24 (d)

Table of Contents

General Surveys.- A Unified Language for Mathematics and Physics.- Clifford Algebras and Spinors.- Classification of Clifford Algebras.- Pseudo-Euclidean Hurwitz Pairs and Generalized Fueter Equations.- A New Representation for Spinors in Real Clifford Algebras.- Primitive Idempotents and Indecomposable Left Ideals in Degenerate Clifford Algebras.- Spin Groups.- Groupes de Clifford et Groupes des Spineurs.- Algebres de Clifford Cr,s+ des Espaces Quadratiques Pseudo-Euclidiens standards Er,s et structures correspondantes sur les espaces de Spineurs Associes. Plongements Naturels des Quadratiques Projectives Reelles Q(E r,s) attachees aux Espaces Er,s.- Spin Groups associated with Degenerate Orthogonal Spaces.- Algebres de Clifford Separables II.- Sur une Question de Micali-Villamayor.- Clifford Analysis.- Spingroups and Spherical Monogenies.- Left Regular Polynomials in Even Dimensions, and Tensor Products of Clifford Algebras.- Spingroups and Spherical Means.- The Biregular Functions of Clifford Analysis: Some Special Topics.- Clifford Numbers and Möbius Transformations in Rn.- Mathematical Physics.- A Clifford Calculus for Physical Field Theories.- Generalized C-R Equations on Manifolds.- Integral Formulae in Complex Clifford Analysis.- Killing Vectors and Embedding of Exact Solutions in General Relativity.- From Grassmann to Clifford.- Lorentzian Applications of Pure Spinors.- The Poincaré Group.- Minimal Ideals and Clifford Algebras in the Phase Space Representation of Spin-1/2 Fields.- Some Consequences of the Clifford Algebra Approach to Physics.- Physical Models.- Algebraic Ideas in Fundamental Physics from Dirac-algebra to Superstrings.- On Two Supersymmetric Approaches to Quantum Gravity: Clifford Algebra Degeneracy v Extended Objects.- Clifford Algebra and the Interpretation of Quantum Mechanics.- Representation-free Calculations in Relativistic Quantum Mechanics.- Dirac Equation for Bispinor Densities.- Unified Spin Gauge Theory Models.- U(2,2) Spin-Gauge Theory Simplification by Use of the Dirac Algebra.- Spin(8) Gauge Field Theory.- Clifford Algebras, Projective Representations and Classification of Fundamental Particles.- Fermionic Clifford Algebras and Supersymmetry.- On Geometry and Physics of Staggered Lattice Fermions.- A System of Vectors and Spinors in Complex Spacetime and Their Application to Elementary Particle Physics.- Spinors as Components of the Metrical Tensor in 8-dimensional Relativity.- Multivector Solution to Harmonic Systems.- The Importance of Meaningful Conservation Equations in Relativistic Quantum Mechanics for the Sources of Classical Fields.- Electromagnetism.- Electromagnetic Theory and Network Theory using Clifford Algebra.- Remarks on Clifford Algebra in Classical Electromagnetism.- Quaternionic Formulation of Classical Electromagnetic Fields and Theory of Functions of a Biquaternion Variable.- Comparison of Clifford and Grassmann Algebras in Applications to Electromagnetics.- Generalisations of Clifford Algebra.- Symplectic Clifford Algebras.- Walsh Functions, Clifford Algebras and Cayley-Dickson Process.- Z(N)-Spin Systems and Generalised Clifford Algebras.- Generalized Clifford Algebras and Spin Lattice Systems.- Clifford Algebra, its Generalisations and Physical Applications.- Application of Clifford Algebras to *-products.- On Regular Functions of a Power-associative Hypercomplex Variable.- On a Geometric Torogonal Quantization Scheme.
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