Advertisement

Clifford Algebras and their Applications in Mathematical Physics

Volume 1: Algebra and Physics

  • Rafał Abłamowicz
  • Bertfried Fauser

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

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Physics: Applications and Models

    1. Front Matter
      Pages 1-1
    2. Tevian Dray, Corinne A. Manogue
      Pages 21-37
    3. Kurt Just, James Thevenot
      Pages 39-48
    4. Antony Lewis, Anthony Lasenby, Chris Doran
      Pages 49-71
  3. Physics: Structures

  4. Geometry and Logic

    1. Front Matter
      Pages 155-155
    2. Bernd Schmeikal
      Pages 219-241
  5. Mathematics: Deformations

    1. Front Matter
      Pages 243-243
    2. Gaetano Fiore
      Pages 269-282
    3. Marcos Rosenbaum, J. David Vergara
      Pages 283-302
  6. Mathematics: Structures

    1. Front Matter
      Pages 321-321
    2. Bertfried Fauser, Rafał Abłamowicz
      Pages 341-366
    3. Virginia V. Fernández, Antonio M. Moya, Waldyr A. Rodrigues Jr.
      Pages 367-391
    4. Zbigniew Oziewicz, José Ricardo R. Zeni
      Pages 425-433
  7. Back Matter
    Pages 449-461

About this book

Introduction

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.

Keywords

Mathematica Spinor algebra clifford algebra cohomology differential equation dynamics geometry invariant manifold mathematical physics mathematics operator solution theory of relativity

Editors and affiliations

  • Rafał Abłamowicz
    • 1
  • Bertfried Fauser
    • 2
  1. 1.Department of MathematicsTennessee Technological UniversityCookevilleUSA
  2. 2.Fachbereich PhysikUniversität KonstanzKonstanzGermany

Bibliographic information

Industry Sectors
Aerospace
Oil, Gas & Geosciences