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Clifford Algebras and their Applications in Mathematical Physics

Volume 1: Algebra and Physics

  • Book
  • © 2000

Overview

Editors:
  1. Rafał Abłamowicz

    1. Department of Mathematics, Tennessee Technological University, Cookeville, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Bertfried Fauser

    1. Fachbereich Physik, Universität Konstanz, Konstanz, Germany

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Mathematical Physics (PMP, volume 18)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xxv
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  2. Physics: Applications and Models

    1. Front Matter

      Pages 1-1
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    2. Multiparavector Subspaces of Cℓn: Theorems and Applications

      • William E. Baylis
      Pages 3-20

    3. Quaternionic Spin

      • Tevian Dray, Corinne A. Manogue
      Pages 21-37

    4. Pauli Terms Must Be Absent in the Dirac Equation

      • Kurt Just, James Thevenot
      Pages 39-48

    5. Electron Scattering in the Spacetime Algebra

      • Antony Lewis, Anthony Lasenby, Chris Doran
      Pages 49-71

  3. Physics: Structures

    1. Front Matter

      Pages 73-73
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    2. Twistor Approach to Relativistic Dynamics and to the Dirac Equation — A Review

      • Andreas Bette
      Pages 75-92

    3. Fiber with Intrinsic Action on a 1 + 1 Dimensional Spacetime

      • Robert W. Johnson
      Pages 93-100

    4. Dimensionally Democratic Calculus and Principles of Polydimensional Physics

      • William M. Pezzaglia Jr.
      Pages 101-123

    5. A Pythagorean Metric in Relativity

      • Franco Israel Piazzese
      Pages 125-133

    6. Clifford-Valued Clifforms: A Geometric Language for Dirac Equations

      • Jose G. Vargas, Douglas G. Torr
      Pages 135-154

  4. Geometry and Logic

    1. Front Matter

      Pages 155-155
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    2. The Principle of Duality in Clifford Algebra and Projective Geometry

      • Oliver Conradt
      Pages 157-193

    3. Doing Geometric Research with Clifford Algebra

      • Hongbo Li
      Pages 195-217

    4. Clifford Algebra of Quantum Logic

      • Bernd Schmeikal
      Pages 219-241

  5. Mathematics: Deformations

    1. Front Matter

      Pages 243-243
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    2. Hecke Algebra Representations in Ideals Generated by q-Young Clifford Idempotents

      • Rafał Abłamowicz, Bertfried Fauser
      Pages 245-268

    3. On q-Deformations of Clifford Algebras

      • Gaetano Fiore
      Pages 269-282

    4. Dirac Operator, Hopf Algebra of Renormalization, and Structure of Spacetime

      • Marcos Rosenbaum, J. David Vergara
      Pages 283-302
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Keywords

About this book

The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po­ sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans­ lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois­ son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.

Editors and Affiliations

  • Department of Mathematics, Tennessee Technological University, Cookeville, USA

    Rafał Abłamowicz

  • Fachbereich Physik, Universität Konstanz, Konstanz, Germany

    Bertfried Fauser

Bibliographic Information

  • Book Title: Clifford Algebras and their Applications in Mathematical Physics

  • Book Subtitle: Volume 1: Algebra and Physics

  • Editors: Rafał Abłamowicz, Bertfried Fauser

  • Series Title: Progress in Mathematical Physics

  • DOI: https://doi.org/10.1007/978-1-4612-1368-0

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • Hardcover ISBN: 978-0-8176-4182-5Published: 15 June 2000

  • Softcover ISBN: 978-1-4612-7116-1Published: 16 October 2012

  • eBook ISBN: 978-1-4612-1368-0Published: 06 December 2012

  • Series ISSN: 1544-9998

  • Series E-ISSN: 2197-1846

  • Edition Number: 1

  • Number of Pages: XXV, 461

  • Topics: Differential Geometry, Mathematical Methods in Physics, Theoretical, Mathematical and Computational Physics

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