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 (∝4000 types) than the known supersymmetric ones (∝200). (orig.)