A Large Deviation Principle for Symmetric Markov Processes with Feynman-Kac Functional

We establish a large deviation principle for the occupation distribution of a symmetric Markov process with Feynman-Kac functional. As an application, we show the L^p-independence of the spectral bounds of a Feynman-Kac semigroup. In particular, we consider one-dimensional diffusion processes and show that if no boundaries are natural in Feller's boundary classification, the L^p-independence holds, and if one of the boundaries is natural, the L^p-independence holds if and only if the L²-spectral bound is non-positive.