Electric vector potentials and the effective lagrangian for long distance Yang-Mills theory

Abstract

We use electric vector potentials, originally introduced by Mandelstam, to describe long distance SU(2) Yang-Mills theory. We require that the effective long distance lagrangian is the simplest gauge invariant expression involving these potentials which yields a 1 q 4 gluon propagator in the abelian limit. From the resulting lagrangian we obtain equations of motion with solutions corresponding to tubes of electric color flux quantized in units of e 2 ( e is the Yang-Mills coupling constant). This is the criterion for electric confinement of color.