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

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

1994-07-05

arxiv.org/abs/hep-ph/9407222v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

Latex, 23 pages. no figures, ISU-IAP.Th94-02, Irkutsk

Scientific paper

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.

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