On triviality of the :exp λϕ: 4 quantum field theory in a finite volume

Abstract

The ʃ dν(λ):exp λϕ: n (without counterterms) quantum field theory is considered. Here ν(·) is a finite positive measure. Let n ⩾ 3, or n = 2 and supp ν ∩ [− 8π , 8π ] = ∅ . Under these conditions the theory ʃ dν(λ):exp λϕ: n (without counterterms)converges to the free-field theory when the cut- offs are removed.