EXPLICIT CONSTRUCTION OF THE RENORMALIZATION GROUP TRANSFORMATIONS IN PHI-4 FIELD-THEORY

The counterterms of a φ{symbol}4 quantum field theory are decomposed into contributions corresponding to forests of divergent generalized vertices. A partial summation of the perturbation series may be performed according to the forests. An intrinsic representation of the elements of the renormalization group is obtained under the form of the exponential of a differential operator. If we solve the corresponding differential equation, we obtain an integral representation for the multiplicative renormalization. The knowledge of such a summation process is useful to the study of any asymptotic behaviour (Regge behaviour, infrared behaviour...) in a strictly renormalizable field theory. © 1979.