On geometrical representation of the Jacobian in a path integral reduction problem

Details On geometrical representation of the Jacobian in a path integral reduction problem On geometrical representation of the Jacobian in a path integral reduction problem

2007-12-19

arxiv.org/abs/0712.3278v1

Physics

Mathematical Physics

8 pages

Scientific paper

10.1016/j.physleta.2008.09.017

The geometrical representation of the Jacobian in the path integral reduction problem which describes a motion of the scalar particle on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple Lie group is obtained. By using the formula for the scalar curvature of the manifold with the Kaluza--Klein metric, we present the Jacobian as difference of the scalar curvature of the total space of the principal fibre bundle and the terms that are the scalar curvature of the orbit space, the scalar curvature of the orbit, the second fundamental form of the orbit and the square of the principle fibre bundle curvature.

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