Various Aspects of Divergent Electromagnetic Masses: Analyticity, Scaling, and Light-Cone

Abstract

Various features associated with the divergent electromagnetic self-mass of a particle are elucidated. Bjorken's original analysis is implemented with a simple convergence theorem which serves as a basis on which various models are discussed regarding their implications on the divergence problem as well as on the scaling property. A simple model of the current commutator function is proposed, on the basis of which it is argued that the quark-model light-cone commutator gives a wrong sign to the divergent self-mass due to its lack of the current conservation. It is also shown that it is the next-to-leading singularities on the light-cone of the commutator that bring forth a (logarithmically) divergent mass shift.