Green’s Functions of Field Theory

Abstract

The discussion in this chapter is restricted to Green's function techniques as applied to problems in atomic physics, specifically to the calculation of higher order (correlation, Breit, as well as radiative) corrections to energy levels, and also of transition amplitudes for radiative transitions of atoms which are gauge invariant (GI) at every level of approximation.Green's functiongaugeinvarianceelectron correlationGreen's function techniques forHartree–Fockapproximationrandom phase approximation Green's function techniques were first applied to many-electron atoms in 1971 as specific instances of the use of field theory techniques in many-particle problems 1 ; 2. They initially provided alternative derivations of known approximations such as the Hartree–Fock (HF) approximation and random phase approximation (RPA). The starting point for the derivations was a nonrelativistic (NR) field-theoretical effective Hamiltonian for the system, which involved the nucleus–electron potential and only Coulomb interactions between electrons.