OPTIMIZED DELTA-EXPANSION AND TRIVIALITY OR NONTRIVIALITY OF FIELD-THEORIES

We use a very simple version of the optimized (linear) delta-expansion by scaling the free part of the Lagrangian with a variational paramet er. This method is well suited to calculate the renormalized coupling constant in terms of the free one and the cutoff. One never has to cal culate any new Feynman graphs but simply can modify existing results f rom the literature. We find that Phi(4)(4)-theory as well as QED are f ree in the limit where the cutoff goes to infinity. In contrast to thi s, the structure of Yang-Mills theories enforces a special choice of t he Lagrangian of the delta-expansion. Together with the change in the sign of the beta-function, this leads to a different behavior and allo ws Yang-Mills theory to become non trivial.