Analytic properties of finite-temperature self-energies

The analytic properties in the energy variable k₀ 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 k₀=±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.