On Feenberg's Perturbation Formula

Farhad H. M. Faisal

H. Keiter, Srećko Kilić

Abstract Brillouin‐Wigner (BW) perturbation formulae can be rearranged into a form first proposed by Feenberg. Feenberg's perturbation formulae also follow from a variational principle. They are successfully tested at two typical problems, for which ordinary perturbation techniques completely fail. The first is to find conditions for the bosonization of the Tomonaga model perturbatively. The second is to clarify whether non‐Fermi liquid behavior of the momentum distribution function of the Luttinger model can be achieved perturbatively.

Srećko Kilić, C. E. Campbell

Eleftherios N. Economou

Ishida, K.

We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a generalization of the Brillouin-Wigner perturbation theory and the calculations of their diagonal elements can naturally give the effective propagators which are equal to the ones in the Feenberg perturbation theory.