The renormalized ${\varphi }_4^4$-trajectory by perturbation theory in a running coupling II: the continuous renormalization group

Abstract

The renormalized trajectory of massless ${\varphi }^4$-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 ${\varphi }^4$-interaction. We use an exact functional differential equation for its dependence on the running ${\varphi }^4$-coupling. It is solved by means of perturbation theory. The expansion is proved to be finite to all orders. The proof includes a large momentum bound on amputated connected momentum space Green's functions.

26 pages LaTeX2e

References in corpus (1)

• The renormalized ${\varphi }_4^4$-trajectory by perturbation theory in the running coupling

Cited by in corpus (2)

• Gauge Consistent Wilson Renormalization Group I: Abelian Case
• Renormalized $g-log(g)$ double expansion for the invariant ${\varphi }^4$-trajectory in three dimensions