Clifford Algebras and Spinor Structures

1. Dirac Operator, Maxwell’s Equations, and Conformal Covariance

   1. Biquaternionic Formulation of Maxwell’s Equations and their Solutions

      • K. Imaeda

      Pages 265-280

   2. The Massless Dirac Equation, Maxwell’s Equation, and the Application of Clifford Algebras

      • Peter Morgan

      Pages 281-300

   3. The Conformal Covariance of Huygens’ Principle-Type Integral Formulae in Clifford Analysis

      • John Ryan

      Pages 301-310

2. Clifford Analysis, Boundary Value Problems, Hermite Interpolants, and Padé Approximants

   1. Front Matter

      Pages 311-311

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   2. Cliffor-Valued Functions in Cl ₃

      • W. E. Baylis, Bernard Jancewicz

      Pages 313-324

   3. Clifford-Analysis and Elliptic Boundary Value Problems

      • Klaus Gürlebeck, Wolfgang Sprössig

      Pages 325-334

   4. A Complete Boundary Collocation System

      • Frank Kippig

      Pages 335-342

   5. On the Algebraic Foundations of the Vector є-Algorithm

      • D. E. Roberts

      Pages 343-361

3. Clifford Algebras and Generalization

   1. Front Matter

      Pages 363-363

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   2. Classical Spinor Structures on Quantum Spaces

      • Mićo Đurđević

      Pages 365-377

   3. A Unified Metric

      • Bruce M. Kemmell

      Pages 379-385

   4. Quantum Braided Clifford Algebras

      • Julian Ławrynowicz, Loucas C. Papaloucas, Jakub Rembieliński

      Pages 387-395

   5. Clifford Algebra for Hecke Braid

      • Zbigniew Oziewicz

      Pages 397-411

4. Back Matter

   Pages 413-425

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This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.

• Dirac equation
• Maxwell's equation
• algebra
• clifford algebra
• complex analysis
• differential geometry
• eigenvalue
• field
• geometry
• linear algebra
• manifold
• mechanics
• quantum mechanics

• Gannon University, Erie, USA

  Rafał Ablamowicz

• Helsinki University of Technology, Espoo, Finland

  Pertti Lounesto

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