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The Dyson equation:

[tex] G = G_0 + G_0 V G[/tex] usually solved with the iteration steps [tex] G_{j+1} = G_0 + G_0 V G{j}[/tex]

The Heisenberg equation of motion (with the density as the operator):

[tex] \rho = U^{\dag} \rho_0 U{ [\tex] with [tex] U = e^{\frac{-i}{\hbar} H t[\tex] (in the case of a time independent Hamiltonian).

There must be bridge, but I can't find a mathematical transition or a common ground. My knowledge on Green's function is just too limited.

Does anybody has an idea what could lead in the right direction?