Perturbation theory and the energy spectrum of normal Fermi systems

This paper is a study in a possible steady-state perturbation theory for ar bitrary excited multiply degenerate states of a normal Fermi system in the statistical limit. An operator technique has been developed to transform th e relevant Hamiltonian into an operator that is a function of occupation nu mber operators only. The perturbation theory equations have been proved to be solvable in the space of quasinormal form operators and their formal sol utions have been derived. It is shown that the operator series of perturbat ion theory can be transformed to a linked cluster expansion with the nonphy sical powers of volume eliminated. Elimination of nonphysical terms is effe cted without use of the diagrams technique. (C) 2001 American Institute of Physics.