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. For a main approximation, the self-consistent field model that considers to a certain degree forces caused by interaction of fields is chosen. This approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of fermion mass in the process of interaction with exchange by a scalar boson is investigated. It is demonstrated that for zero bare mass, the fermion can acquire mass only if its coupling constant exceeds the critical value determined by the boson mass. In this regard, the problem of the neutrino mass is discussed.