Particle propagation on a circle with a point interaction

We study a particle propagation on a circle in the presence of a point interaction. We show that the one-particle Feynman kernel can be written as the sum of reflected and transmitted trajectories which are weighted by the elements of the nth power of the scattering matrix evaluated on a line with a point interaction. As a by-product, we find a three-parameter family of trace formulae as a generalization of the Poisson summation formula