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A system composed of two-level systems interacting with a single excitationof a one-dimensional boson field with continuous spectrum, described by aFriedrichs (or Friedrichs-Lee) model, can exhibit bound states and resonances;the latter can be characterized by computing the so-called self-energy of themodel. We evaluate an analytic expression, valid for a large class ofdispersion relations and coupling functions, for the self-energy of suchmodels. Afterwards, we focus on the case of identical two-level systems, and werefine our analysis by distinguishing between dominant and suppressedcontributions to the associated self-energy; we finally examine thephenomenology of bound states in the presence of a single dominantcontribution.

The self-energy of Friedrichs-Lee models and its application to bound states and resonances