Modified perturbation theory for the Yukawa model

Abstract

A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for the effects caused by the interaction of fields. Such choice of the main approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of the fermion mass due to the interaction with exchange of the scalar boson is investigated. It is demonstrated that, for zero bare mass, the fermion can acquire mass only if the coupling constant exceeds the critical value determined by the boson mass. In this connection, the problem of the neutrino mass is discussed.