LOCAL COUPLINGS, DOUBLE INSERTIONS AND THE WEYL CONSISTENCY CONDITION

Within massless phi4(4)-theory we set up the formalism which is needed , when the coupling lambda is permitted to become an external field, i .e. a function of space-time. In particular we have worked out the act ion of the corresponding Callan-Symanzik operator and conformal transf ormations on the vertex functions, and furthermore how the Weyl transf ormations act on the theory with the energy-momentum tensor invariantl y coupled. With the help of the Weyl consistency condition we have sho wn that in the limit of constant coupling the Weyl breaking can entire ly be written in terms of differential operators, but that otherwise, for truly local coupling, new breaking terms survive.