Existence of the Schwinger Functions of the Three-Dimensional Gross-Neveu Model

One of the conclusions of previous rigorous studies on renormalization theory is that the concept of perturbative renormalizability shall not be considered as a fundamental requirement for a quantum field model to exist. Indeed, to solve the question of the ultraviolet (UV) limit, ρ → ∞, of a model presenting a set of parameters Ω _ρ [ρ labelling an UV cutoff], in most cases one must drop out completely the traditional intermediate step involving a Taylor expansion in the coupling constant and properly ask whether or not one can prescribe functions for the parameters appearing in Ω _ρ , in terms of the variable ρ and the set Ω _ren of (finite and often positive) renormalized parameters, such that the n-point Schwinger (correlation) functions S _n,ρ exist when ρ → ∞ and describe a non-trivial (interacting) system.