Poisson wave trace formula for Dirac resonances at spectrum edges and applications

We study the self-adjoint Dirac operators D = D0 + V (x), where is free three-dimensional operator and (x) a smooth compactly supported Hermitian matrix potential. define resonances of as poles meromorphic continuation its cut-off resolvent. By analyzing resolvent behaviour at spectrum edges ±m, we establish generalized Birman-Krein formula, taking into account possible ±m. As an application new formula Poisson wave trace in full generality. The links with difference groups. conjunction asymptotics scattering phase, allows us to prove that, under certain natural assumptions on , perturbed has infinitely many resonances; result similar nature Melrose’s classic 1995 for Schr¨odinger operators.