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

Abstract

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

arXiv comment12 pages, LaTex

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