Analytic characterization of conditional gaugeability for non-local Feynman-Kac transforms

An analytic characterization of gaugeability and conditional gaugeability is given for non-local (or discontinuous) Feynman-Kac transforms of general symmetric Markov processes. This analytic characterization is very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases.