Perturbative renormalization of ϕ44 theory on the half space R+×R3 with flow equations

Abstract

In this paper, we give a rigorous proof of the renormalizability of the massive [Formula: see text] theory on a half-space using renormalization group flow equations. We find that five counterterms are needed to make the theory finite, namely, ϕ2, ϕ∂ z ϕ, [Formula: see text], ϕΔ x ϕ, and ϕ4 for [Formula: see text]. The amputated correlation functions are distributions in position space. We consider a suitable class of test functions and prove inductive bounds for the correlation functions folded with these test functions. The bounds are uniform in the cutoff and, thus, directly lead to renormalizability.