||IHEP 98 - 1
|Bogolubov Transformation in Path Integrals on Manifolds with a Group Action|
|Protvino, 1998.- p.25, refs.:17.|
A path integral with respect to the measure, generated by the stochastic process, is used to describe the particle motion on a compact Riemannian manifold, on which a free effective and isometric action of a compact semi-simple Lie group is given.
By choosing with the Bogolubov coordinate transformation method the coordinates, adapted to the principal fibre structure, the transformation of the path integral is performed. The separation of variables in the obtained path integral is realized with the help of the nonlinear filtering equation from the stochastic process theory.
After factorizing the path integral measure, we get the integral relation between the path integral given on the total space of the principal fiber bundle and the path integral on the base space of this bundle --- the orbit space of the group action.
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