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Lorentz-Covariant Hamiltonian Formalism

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Abstract

The dynamics of a classical system can be expressed by means of Poissonbrackets. In this paper we generalize the relation between the usual noncovariantHamiltonian and the Poisson brackets to a covariant Hamiltonian and new bracketsin the frame of Minkowski space. These brackets can be related to those usedby Feynman in his derivation Maxwell's equations. The case of curved space isalso considered with the introduction of Christoffel symbols, covariant derivatives,and curvature tensors.

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Authors and Affiliations

  1. L.P.L.I. Institut de Physique, 57070, Metz, France

    A. Bérard & H. Mohrbach

  2. Institut Fourier, UMR 5582 CNRS, UFR de Mathématique, Université Grenoble I, 38402, Saint Martin d'Héres, Cedex, France

    P. Gosselin

Authors
  1. A. Bérard
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  2. H. Mohrbach
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  3. P. Gosselin
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Bérard, A., Mohrbach, H. & Gosselin, P. Lorentz-Covariant Hamiltonian Formalism. International Journal of Theoretical Physics 39, 1055–1068 (2000). https://doi.org/10.1023/A:1003654525047

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  • DOI: https://doi.org/10.1023/A:1003654525047

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