Running coupling expansion for the renormalized $\phi^4_4$-trajectory   from renormalization invariance
  We formulate a renormalized running coupling expansion for the $\beta$--function and the potential of the renormalized $\phi^4$--trajectory on four dimensional Euclidean space-time. Renormalization invariance is used as a first principle. No reference is made to bare quantities. The expansion is proved to be finite to all orders of perturbation theory. The proof includes a large momentum bound on the connected free propagator amputated vertices. 
Christian Wieczerkowski (University of Muenster)