The renormalized Φ44 trajectory by perturbation theory in a running coupling (II). The continuous renormalization group Original Research Article

The renormalized trajectory of massless Φ4 theory on four-dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the Φ4 interaction. We use an exact functional differential equation for its dependence on the running Φ4 coupling. It is solved by means of perturbation theory. The expansion is proven to be finite to all orders. The proof includes a large momentum bound on amputated connected momentum space Green functions.