Condensed Matter Physics, 1998, vol. 1, No. 3, p. 593-604, English

Authors:J.Darewych (Department of Physics and Astronomy, York University, Toronto, Ontario, M3J 1P3, Canada)

We consider a reformulation of the Yukawa model, in which fermions interact via a mediating (massive or massless) scalar field. Covariant Green functions are used express the mediating field in terms of the fermion fields. The resulting Hamiltonian of the theory has an interaction term in which the propagator of the mediating field appears directly. We show that if processes involving emission of physical mediating field quanta can be ignored and an unconventional empty vacuum is used, then exact few-fermion eigenstates of the resulting truncated Hamiltonian can be obtained in the canonical equal-time formalism. These eigenstates lead to two- and three-body Dirac-like equations with scalar interactions. Two-fermion bound states are obtained by the numerical solution of the eigenvalue equation for $J=0$ states. Comparison is made with conventional treatments of this model.

Key words: few-fermion systems, Yukawa model, mass spectrum
Comments: Figs. 0, Refs. 11, Tabs. 2.

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