A geometric generalization of classical mechanics and quantization
A geometrization of classical mechanics is presented which may be considered as a realization of the Hertz picture of mechanics. The trajectories in thef-dimensional configuration spaceVf of a classical mechanical system are obtained as the projections onVf of the geodesics in an (f + 1) dimensional Riemannian spaceVf + 1, with an appropriate metric, if the additional (f + 1)th coordinate, taken to be an angle, is assumed to be “cyclic”.
When the additional (angular) coordinate is not cyclic we obtain what may be regarded as a generalization of classical mechanics in a geometrized form. This defines new motions in the neighbourhood of the classical motions. It has been shown that, when the angular coordinate is “quasi-cyclic”, these new motions can be used to describe events in the quantum domain with appropriate periodicity conditions on the geodesics inVf + 1.
Volume 93 | Issue 5
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