An Ultraviolet Finite Theory of Scalars

We construct a theory of scalars that is free of short-distance infinities to all orders in perturbation theory. Loop divergences are neutralized by momentum-dependent interactions that are ghost free and polynomially bounded. The finite counterparts of the usual one-loop scalar self-energy and beta function are straightforwardly computed. In a variant of this model, the one-loop mass renormalization is zero due to an inversion that swaps the ultraviolet and the infrared.