Analytic Structure of Energy Levels in a Field-Theory Model

We consider a model of λφ⁴ field theory in which perturbation theory diverges and analytically continue the energy levels into the complex λ plane. Using WKB technique, we determine that the energy levels have an infinite sequence of branch points (where level crossing occurs) with a limit point aλ=0. Thus the origin is not an isolated singularity. The resolvent (z-H)^-1 has an infinite sequence of poles with a limit point at λ=0.