ON THE DEFINITION OF QUASI-AVERAGES FOR A HAMILTONIAN WITH NEGATIVE FOUR-FERMION INTERACTION

N. N. Bogolyubov

Ph. Ghez

Joseph N. Ginocchio

Nikolay N. Bogolubov, Andrey Vladimirovich Soldatov

An approach is proposed which allows one to investigate dynamical and thermodynamical properties of models with four-fermion interaction of general type. The approach combines ideas of the standard Bogolubov's approximating Hamiltonian method for the models with separable interaction with the method of Hartree–Fock approximation based on the ideas of self-consistency.

Andrei Dolocan, Voicu Dolocan, Voicu Dolocan

Using the Lagrangian formalism we attempt to introduce a new Hamiltonian for fermions. On this basis we have evaluated the expectation values for the interaction energy between fermions via bosons. The interaction energy between two fermions via phonons becomes attractive in a degenerate fermion-gas. The interaction energy between two fermions via photons appears to be attractive in certain conditions. The self-energy of the fermion + boson system, e.g. polaron and polariton, was evaluated.