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