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We study the $\frac{\lambda}{4!}\phi^{4}$ massless scalar field theory in afour-dimensional Euclidean space, where all but one of the coordinates areunbounded. We are considering Dirichlet boundary conditions in two hyperplanes,breaking the translation invariance of the system. We show how to implement theperturbative renormalization up to two-loop level of the theory. First,analyzing the full two and four-point functions at the one-loop level, we shownthat the bulk counterterms are sufficient to render the theory finite.Meanwhile, at the two-loop level, we have to introduce also surfacecounterterms in the bare lagrangian in order to make finite the full two andalso four-point Schwinger functions.Comment: 14 pages, LaTe

The two-loop massless (λ∕4!)φ4 model in nontranslational invariant domain