Running coupling expansion for the renormalized ${\varphi }_4^4$-trajectory from renormalization invariance

Abstract

We formulate a renormalized running coupling expansion for the $\beta$--function and the potential of the renormalized ${\varphi }^4$--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.

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