Renormalization Analysis for Degenerate Ground States

We consider a Hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons. We show that the ground state projection and the ground state energy are analytic functions of the coupling constant in a cone with apex at the origin, provided a mild infrared assumption holds. To show the result operator theoretic renormalization is used and extended to degenerate situations.