Continuity properties of Schrodinger semigroups with magnetic fields

The objects of the present study are one-parameter semigroups generated by Schodinger operators with fairly general electromagnetic potentials. More p recisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multidimensional Euclidean sp ace; in case that it is a proper subset, the Schrodinger operator is render ed symmetric by imposing Dirichlet boundary conditions. We discuss the cont inuity of the image functions of the semigroup and show local-norm-continui ty of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. A ltogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Sec. 7 (1982) 447] to non-zero vector po tentials and more general configuration spaces.