Foundations of Physics

, Volume 11, Issue 3–4, pp 307–328 | Cite as

De-Rham currents and charged particle interactions in electromagnetic and gravitational fields

  • C. T. J. Dodson
  • R. W. Tucker


A coordinate-free formulation is established for (semi) classical particle-field interactions. The exterior language of spacetime chains and De-Rham currents enables the description to include extended strings and membranes besides point particles. Treating physical fields in terms of sections of particular bundles, a unified account of interactions is presented in terms of an intrinsic action principle on a bundle of jets over spacetime. The theory is illustrated by considering the specific model of point particles with intrinsic spin covariantly coupled to theU(1) andSL(2, C) connections describing the electromagnetic and gravitational fields, respectively. The notion of dual spin is examined in this context and coupled equations for this particle-field system are explicitly derived in a local chart. Attention is drawn to the global implications of the theory.


Charged Particle Specific Model Gravitational Field Particle Interaction Action Principle 
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  1. 1.
    P. A. Collins and R. W. Tucker,Nucl. Phys. B 112 150 (1976); P. S. Howe and R. W. Tucker,J. Math. Phys. 19, 981 (1978).Google Scholar
  2. 2.
    E. Lubkin,Ann. Phys. (N.Y.) 23, 233 (1963); J. S. Dowker and J. A. Roche,Proc. Phys. Soc. 92, 1 (1967).Google Scholar
  3. 3.
    P. A. M. Dirac,Phys. Rev. 74, 817 (1948).Google Scholar
  4. 4.
    C. T. J. Dodson and T. Poston,Tensor Geometry (Pitman, London, 1977).Google Scholar
  5. 5.
    Y. Choquet-Bruhat, C. de Witt-Morette, and M. Dillard-Bleick,Analysis, Manifolds and Physics (North-Holland, 1977).Google Scholar
  6. 6.
    C. T. J. Dodson,Categories, Bundles and Spacetime Topology (Shiva, Orpington, Kent, 1980).Google Scholar
  7. 7.
    S. Kobayashi and K. Nomizu,Foundations of Differential Geometry (Interscience, 1963), Vol. 1.Google Scholar
  8. 8.
    M. Daniel and C. M. Viallet,Rev. Mod. Phys. 52, 175 (1980); W. Drechsler and M. E. Meyer,Fibre Bundle Techniques in Gauge Theories (Springer Verlag, No. 67, 1977.Google Scholar
  9. 9.
    G. De-Rham,Variétés Différentiables (Hermann, Paris, 1960).Google Scholar
  10. 10.
    V. Aldaya and J. A. de-Azcárraga,J. Math. Phys. 19, 1869 (1978); M. W. Hirsch,Differential Topology (Springer Verlag, 1976); R. S. Palais,Foundations of Global Non-Linear Analysis (W. Benjamin, 1968).Google Scholar
  11. 11.
    R. W. Tucker,J. Math. Phys., to be published; I. M. Benn, T. Dereli, and R. W. Tucker, Double Dual Solutions of Generalised Theories of Gravitation,J. Gen. Rel. Grav., to be published.Google Scholar
  12. 12.
    A. Papapetrou,Proc. Roy. Soc. A 209, 248 (1951); H. Künzle,Comm. Math. Phys. 27, 23 (1972); A. Barducci, R. Casalbuoni, and L. Lusanna,Nucl. Phys. B 124, 521 (1977); C. J. S. Clarke,Gen. Rel. Grav. 2, 43 (1971).Google Scholar
  13. 13.
    P. A. Collins and R. W. Tucker,Phys. Lett. 64B, 207 (1976); L. Brink, S. Deser, B. Zumino, P. di Vecchia, and P. Howe,Phys. Lett. 64B, 435 (1976); P. A. Collins and R. W. Tucker,Nucl. Phys. B 121, 307 (1979).Google Scholar
  14. 14.
    I. M. Benn, T. Dereli, and R. W. Tucker, Gravitational Monopoles with Classical Torsion,J. Phys. A: Math. 13, 359 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • C. T. J. Dodson
    • 1
  • R. W. Tucker
    • 2
  1. 1.Department of MathematicsUniversity of LancasterLancasterEngland
  2. 2.Department of PhysicsUniversity of LancasterLancasterEngland

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