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IHEP 2000 - 54
(In Russian)
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| S.N.Storchak | |||
Path Integral Measure Factorization
when Exploiting the Dependent Coordinates Reduction
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Protvino, 2000.-p.24, refs.:22.
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The reduction procedure in the Wiener-type
path integrals for the diffusion on a smooth compact
Riemannian manifold with
the given free isometric
action of the compact semi--simple unimodular
Lie group is considered.
The investigation is carried out in the case
when
the dependent coordinates defined
by an optional
gauge surface and the group coordinates
are used in an arising
principal fiber bundle that is assumed to be trivial.
The transformation
of the
path integral on a principle fiber bundle,
which factorizes the path integral measure,
applies the
optimal nonlinear filtering equation from
the stochastic theory.
As a result of the path integral transformations
the integral relation between the kernels of
the original
and reduced semigroups are obtained.
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