Brillouin-Wigner and Feenberg perturbation methods in many-body theory

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.