Existence of Dirac resonances in the semi-classical limit

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials V decaying like < x >(-delta) at infinity for some delta > 0. By studying analytic singularities of a certain distribution related to V and by combining two trace formulas, we prove that the perturbed Dirac operators possess resonances near sup V + 1 and inf V - 1. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter.