Foundations of Physics

, Volume 10, Issue 11–12, pp 855–863 | Cite as

Clebsch representations and energy-momentum of the classical electromagnetic and gravitational fields

  • G. S. Asanov


By means of a Clebsch representation which differs from that previously applied to electromagnetic field theory it is shown that Maxwell's equations are derivable from a variational principle. In contrast to the standard approach, the Hamiltonian complex associated with this principle is identical with the generally accepted energy-momentum tensor of the fields. In addition, the Clebsch representation of a contravariant vector field makes it possible to consistently construct a field theory based upon a direction-dependent Lagrangian density (it is this kind of Lagrangian density that may arise when developing the Finslerian extension of general relativity). The corresponding field equations are proved to be independent of any gauge of Clebsch potentials. The law of energy-momentum conservation of the field appears to be covariant and integrable in a rather wide class of direction-dependent Lagrangian densities.


Vector Field Electromagnetic Field Lagrangian Density Tensor Field Classical Electromagnetic 
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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • G. S. Asanov
    • 1
  1. 1.Department of Theoretical PhysicsMoscow State UniversityMoscowUSSR

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