Solution of The Heisenberg Equation For The Four-fermion Contact Interaction by The Method of Dynamical Mappings

Vall, A. N.; Leviant, V. M.; Sinitskaya, A. V.

Solution of The Heisenberg Equation For The Four-fermion Contact Interaction by The Method of Dynamical Mappings

Authors

Vall, A. N.

Leviant, V. M.

Sinitskaya, A. V.

Description

In the paper we consider non-relativistic analog of the Nambu-Jona-Lasinio model and demonstrate, by this most simplified example, the method of dynamical mappings of Heisenberg fields on "physical" fields. We obtain the expressions for one particle eigen-excitation spectrum of full Hamiltonian (spectrum of "clad" fermions), wave function of two excitations' bound state and its mass, and compute the Bethe-Solpither amplitude. We derive as well the relation for the density of vacuum energy as a function of mapping parameters. The minimization of energy leads us to the fixation of these parameters. The method admits the generalization on the relativistic case.
Latex, 23 pages. no figures, ISU-IAP.Th94-02, Irkutsk