Analytic Properties of Finite-Temperature Self-Energies
  The analytic properties in the energy variable k_{0} of finite-temperature self-energies are investigated. A typical branch cut results from n particles being emitted into the heat bath and n' being absorbed from the heat bath. There are three main results: First, in addition to the branch points at which the cuts terminate, there are also branch points attached to the cuts along their length. Second, branch points at k_{0}=\pm k are ubiquitous and for massive particles they are essential singularities. Third, in a perturbative expansion using free particle propagators or in a resummed expansion in which the propagator pole occurs at a real energy, the self-energy will have a branch point at the pole location. 
H. Arthur Weldon