Abstract
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.
Similar content being viewed by others
References
H. Rund, in Topics in Differential Geometry (Academic Press, New York, 1976), pp. 111–133.
H. Rund, Arch. Rational Mech. Anal. 65, 305 (1977).
H. Rund, Arch. Rational Mech. Anal. 71. 199 (1979).
R. Baumeister, J. Math. Phys. 19, 2377 (1978).
R. Baumeister, Utilitas Mathematica 18, 189 (1980).
H. Rund and J. H. Beare, Variational Properties of Direction-Dependent Metric Fields (University of South Africa, Pretoria, 1972).
G. S. Asanov, Nuovo Cimento 49B, 221 (1979).
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Addison-Wesley, Reading, Mass., 1962).
H. Rund, The Differential Geometry of Finsler Spaces (Springer-Verlag, Berlin, 1959).
G. S. Asanov, Preprint N 195, Inst. Math. Polish Academy of Sci. (1979), pp. 1–34.
G. S. Asanov, Reports on Math. Phys. 13, 13 (1978).
D. Lovelock and H. Rund, Tensors, Differential Forms and Variational Principles (Wiley, New York, 1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Asanov, G.S. Clebsch representations and energy-momentum of the classical electromagnetic and gravitational fields. Found Phys 10, 855–863 (1980). https://doi.org/10.1007/BF00708684
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00708684