Operator expectation values, self-energies, cutting rules, and higher-order processes

Danielewicz P.

The high-order structure of diagrammatic expansion in real-time many-body theory is examined. The existence of cutting rules is demonstrated for diagrams that can correspond to the expectation values of operator products, self-energies, etc. The rules permit one to express these quantities, as convolutions of retarded amplitudes with the Green’s functions corresponding to densities, extending over the past of a many-body system. The quasiparticle limit of the results is discussed. As an example, the resummation is carried over the repeated interactions between excitations in a medium, for the self-energies that correspond to single- particle absorption and production rates. The imaginary nucleon optical potential, that is used in nuclear physics, is identical with the combination of the rates. Further, the formulae for the absorption and production rates of collective excitations are derived.