The renormalized φ44 trajectory by perturbation theory in a running coupling (II). The continuous renormalization group

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.