Sturm expansions in many-fermion problems

A generalization of the method of Sturm expansions is the basts of a systematic approach proposed for the construction of a complete system of intermediate states in the perturbation problem for stationary states of many-fermion systems. A time-independent expansion of the Green's function is constructed with respect to a complete set of antisymmetric functions, which include quasiparticle excitations of Sturm type. It is shown that in the case of single-particle perturbations one can completely avoid integration over continuum states, and in the case of perturbations that contain two-body interactions the multiplicity of the integrals can be significantly reduced. A diagram technique is developed for calculating the terms of the perturbation theory expansion.