A new improved energy-momentum tensor

Abstract

We show that the matrix elements of the conventional symmetric energy-momentum tensor are cut-off dependent in renormalized perturbation theory for most renormalizable field theories. However, we argue that, for any renormalizable field theory, it is possible to construct a new energy-momentum tensor, such that the new tensor defines the same four-momentum and Lorentz generators as the conventional tensor, and, further, has finite matrix elements in every order of renormalized perturbation theory. (“Finite” means independent of the cut-off in the limit of large cut-off.) We explicitly construct this tensor in the most general case. The new tensor is an improvement over the old for another reason: the currents associated with scale transformations and conformal transformations have very simple expressions in terms of the new tensor, rather than the very complicated ones they have in terms of the old. We also show how to alter general relativity in such a way that the new tensor becomes the source of the gravitational field, and demonstrate that the new gravitation theory obtained in this way meets all the epxerimental tests that have been applied to general relativity.