Regularization of quantum electrodynamics through nonpolynomial Lagrangians

Abstract

A model for regularizing quantum electrodynamics through a nonpolynomial Lagrangian describing the interaction of the electron field with an auxiliary field is given. A gauge-invariant Lagrangian density is obtained. This kind of regularization avoids the difficulties connected with an indefinite metric. Renormalization of quantum electrodynamics is performed for irreducible diagrams. In the hypothesis that this kind of regularization is the physical basis for elimination of divergences in quantum electrodynamics, the physical implications are discussed. In particular, the limits of validity of quantum electrodynamics are discussed in terms of the coupling constant between the electron and the regularizing field. It is found that the present limits of validity of quantum electrodynamics imply for this coupling constant an upper limit larger than the weak-coupling constant. The possibility of regularization through weak interactions is discussed. In this model, for every reasonable coupling constant, the electromagnetic self-mass of the electron is only a fraction of the total mass.