SHORT-DISTANCE BEHAVIOR OF RENORMALIZABLE QUANTUM-FIELD THEORIES

We introduce particular coordinates to the infinite-dimensional theory space (consisting of all possible hamiltonians) of euclidean quantum field theory such that all but a finite number of coordinates vanish for renormalizable theories. With this choice we can analyze the structure of the renormalization group equations by counting scaling dimensions of the coordinates. Following Wegner's idea we combine the renormalization group with the operator product expansion to determine all possible non-analytic dependence on the renormalized coupling constants in the short-distance expansions of the n-point correlation functions.