Comment on the breakdown of dilatation invariance

On the basis of our previous results concerning the breakdown of dilatation invariance we find that two large classes of models in quantum field theory may lead to the same observable quantities in spite of their different properties under scale transformation. Although the conditions of equivalence have long been known we emphasize their relevance in the new context of the dilatation transformation. The equivalence in question leads to the same physical masses, observable coupling constants, and, possibly, to the same energy-momentum tensors associated with the asymptotic fields in the two theories. It is suggested that the arbitrariness in the choice of an interpolating field is a key point for the equivalence of the two theories. Our analysis also underlines the difference between the notions of physical dimension and scale dimension of a field operator.