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Translations and rotations in Riemannian space

  • Physics of Elementary Particles and Field Theory
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Abstract

Vector fields ξi, corresponding to the Poincaré group generators (infinitesimal translations and rotations) are defined by first-order differential conditions. These equations have nontrivial solutions in an arbitrary torsionless Riemannian space, and can be considered as a generalization of the definition of translations and rotations in flat space. The equations for translations can be integrated. For a space with the Minkowski topology, if the boundary conditions at infinity are shown so that the space is asymptotically flat, the solution is unique. The vector fields ξi specify a physical system as a whole.

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Authors and Affiliations

  1. Nuclear Physics Research Institute, M. V. Lomonosov State University, Moscow

    M. E. Gertsenshtein

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  1. M. E. Gertsenshtein
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 3–6, September, 1983.

The author wants to express his gratitude to V. I. Man'ko, to Academician S. P. Novikov, and to Prof. Ya. A. $morodinskii for stimulating discussions.

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Gertsenshtein, M.E. Translations and rotations in Riemannian space. Soviet Physics Journal 26, 773–776 (1983). https://doi.org/10.1007/BF00891836

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  • DOI: https://doi.org/10.1007/BF00891836

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