A Technique for Deriving Green’s Function Approximations

Up to now we have written approximations for G by relying on the propagator interpretations of G and of the G₂ that appears in the equation of motion for G. We have thus been able to write a few simple approximations for G₂ in terms of the processes that we wished to consider. However, physical intuition can take us just so far. The use of purely imaginary times makes a direct interpretation of these equations difficult. Furthermore it is hard to find physical ways of determining the numerical factors that appear in front of the various terms in the expansion of G₂. We therefore seek a systematic way of deriving approximations for G.