NATURAL RENORMALIZATION

A careful analysis of differential renormalization shows that a distin guished choice of renormalization constants allows for a mathematicall y more fundamental interpretation of the scheme. With this set of a pr iori fixed integration constants differential renormalization is most closely related to the theory of generalized functions. The special pr operties of this scheme are illustrated by application to the toy ex a mple of a free massive bosonic theory. Then we apply the scheme to the l-theory. The two-point function is calculated up to five loops. The renormalization group is analyzed and the beta-function and the anomal ous dimension are calculated up to fourth and fifth order, respectivel y. (C) 1997 American Institute of Physics.