Perturbation Theory for Degenerate Problems of Many-Fermion Systems

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Abstract
The linked cluster expansion of the eigenvalues and eigenfunctions of a many-fermion system is extended to the case where the eigenvalues of the unperturbed system are degenerate. It is shown that the eigenvalues and eigenfunctions are to be obtained by solving a secular equation in the space of degenerate unperturbed wave functions; the matrix elements between these unperturbed functions take the form of linked clusters with energy denominators which are the differences of unperturbed energies. Some discussions are given on the relation of this paper to the formalism of Bloch and Horowitz, in which the energy denominators are the differences of an unperturbed energy and the true energy which is to be obtained as the solution to the secular equation.

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