UNIVERSAL CONDITIONS OF FINITENESS FOR GENERAL QUANTUM-FIELD THEORIES

Starting from the observation that a certain quantity F is common to the lowest order finiteness conditions in a general quantum field theory of gauge fields, scalars and fermions, we are led - making massive use of algebraic computer methods - to a new, extremely restrictive condition and eventually to the conjecture that F = 1 for finite theories. All such theories are classified and contain many more interesting candidates for finite theories (approximately 4000 types) than the known supersymmetric ones (approximately 200).