The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals

The theory of infinite dimensional oscillatory integrals by finite dimensional approximations is shown to provide new information on the trace formula for Schrödinger operators. In particular, the explicit computation of contributions given by constant and non constant periodic orbits, for potentials which are quadratic plus a bounded nonlinear part, is provided. The heat semigroup as well as the Schrödinger group are discussed and it is shown in particular that their singular supports are contained in an explicit countable set independent of the bounded part of the potential.