  Nonperturbative dynamic theory has a particular advantage in studying the
transport in a quantum impurity system in a steady state. Here, we develop a
new approach for obtaining the retarded Green's function expressed in resolvent
form. We use the Heisenberg picture to facilitate dynamic theory and propose a
new systematic method of collecting the basis vectors spanning the Liouville
space, which is the most crucial step in obtaining the resolvent Green's
function. We obtain all the linearly independent basis vectors for studying the
single-impurity Anderson models with one and two reservoirs. The latter is an
appropriate model for studying the Kondo phenomenon in a steady state when a
bias is applied. This is one of long standing subjects in theoretical condensed
matter physics.
