Some Interesting Properties of Field theories with an Infinite Number of Fields

摘要

We give an indication that gravity coupled to an infinite number of fieldsmight be a renormalizable theory. A toy model with an infinite number ofinteracting fermions in four-dimentional space-time is analyzed. The model isfinite at any order in perturbation theory. However, perturbation theory isvalid only for external momenta smaller than $\lambda ^{-\frac{1}{2}}$ , where$\lambda$ is the coupling constant.