The Feynman-Kac formula for Schrodinger operators on vector bundles over complete manifolds

作者：Gueneysu Batu

来源：Journal of Geometry and Physics, 2010, 60(12): 1997-2010.

DOI：10.1016/j.geomphys.2010.08.007

• Feynman-Kac formula
• Schrodinger operator
• Riemannian manifold
• Vector bundle
• Magnetic field

Methods from stochastic analysis are combined with functional analytic methods in order to prove a Feynman-Kac formula for Schrodinger type operators with nonnegative locally square integrable potentials on vector bundles over complete Riemannian manifolds. In particular, we obtain a Feynman-Kac-Ito formula on manifolds for Schrodinger operators with magnetic fields.

• 出版日期2010-12