Feynman integrals with point interactions

A Feynman-Kac formula for Schrödinger operators including a one-center point interaction in R3 plus a bounded potential is proved. Functional integration methods on similar Kacʹs averages with point interactions allow us to construct bounded self-adjoint semigroups in L2(R3), with bounded below Schrodinger generators, when V+ ε Lloc2 and V− belongs to a large class of L2 + L−8 potentials. Moreover, a pointwise bound on the range of the semigroup is given.