Yang–Mills field equations for the Coriolis tensor in the n -body problem

The configuration space of a system of n particles has the structure of a principal fiber bundle under the action of the rotation group. In this paper, identities are derived for the curvature of the natural connection on this bundle. These identities are translated into statements about the Corioli...

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Bibliographic Details
Published in:Journal of mathematical physics 1998-02, Vol.39 (2), p.1223-1235
Main Author: Reinsch, Matthias
Format: Article
Language:English
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Summary:The configuration space of a system of n particles has the structure of a principal fiber bundle under the action of the rotation group. In this paper, identities are derived for the curvature of the natural connection on this bundle. These identities are translated into statements about the Coriolis tensor, the local expression for this curvature on the base space of the bundle. The Coriolis tensor is shown to obey field equations of the Yang–Mills type.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.532343