A Feynman-Kac Formula for Unbounded Semigroups

Details A Feynman-Kac Formula for Unbounded Semigroups A Feynman-Kac Formula for Unbounded Semigroups

1999-07-27

arxiv.org/abs/math-ph/9907022v1

Physics

Mathematical Physics

5 pages, LaTeX. To appear in Proc. Intl. Conf. on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Leipzig 1999

Scientific paper

We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x)
that obey (for all \epsilon > 0): V(x) \geq - \epsilon |x|^2 - C_\epsilon. Even
though e^{-tH} is an unbounded operator, any \phi, \psi \in L^2 with compact
support lie in D(e^{-tH}) and <\phi, e^{-tH}\psi> is given by a Feynman-Kac
formula.

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