Theory of bound states of fermions in many-body systems

The problem of two fermions (of species $a$ and $b$) in a many-body system that can contain particles of the same species is considered. The special case of a resonance medium is discussed. The spectrum and damping of the two-particle excitations of the system are determined from the spectral density of the two-particle Green's function. The Bethe–Salpeter equation is used to derive an effective wave equation and an effective two-particle Hamiltonian whose real part determines the spectrum and whose imaginary part determines the damping of the two-particle states. The effective Hamiltonian takes into account the influence of the surrounding medium on the considered pair of particles, this influence being manifested in the form of a dynamic self-energy of the particles, in a modified dynamic interaction, and in exchange effects with fermions of the surrounding medium at finite temperature and density.