Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs

Autoren: Batu Güneysu, Matthias Keller (2020)

We prove a Feynman path integral formula for the unitary group exp(itLv,θ), t0, associated with a discrete magnetic Schrödinger operator Lv,θ on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate


which controls the unitary group uniformly in the potentials in terms of a Schrödinger semigroup, where the potential deg is the weighted degree function of the graph.

Journal d'Analyse Mathematique

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