A Feynman-Kac Formula for Unbounded Semigroups
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/9907022,
title = {A Feynman-Kac Formula for Unbounded Semigroups},
author = {Barry Simon},
journal= {arXiv preprint arXiv:math-ph/9907022},
year = {2007}
}
Comments
5 pages, LaTeX. To appear in Proc. Intl. Conf. on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Leipzig 1999