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IHEP 2005 - 44 (In Russian) | |
|---|---|---|
| S.N.Storchak | ||
| Normal Coordinates in Path Integral Measure Factorization Problems for Dynamical Systems under Reduction | ||
| Protvino, 2005. – p. 20, refs.: 15. | ||
Normal coordinates in the reduction problem of
Wiener path integrals are considered.
The path integrals,
defined by the stochastic processes,
describe the (quantum) motion of a scalar particle on a
smooth compact Riemannian manifold with the given free
proper isometric action of the compact semisimple
unimodular Lee group.
Due to the symmetry of the problem we can
view the manifold as a local fibre space.
It is shown, that the normal coordinates,
as the group coordinates of the principal fiber bundle,
can be used in the path integral measure
factorization method, which is based on the nonlinear
filtering
stochastic differential equation.
The representation of the local
Green functions in terms of the orbit space path integrals
is obtained.
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