Framework for finite alternative theories to a quantum field theory

Abstract

Using the path-integral formalism, we generalize the 't Hooft-Veltman method of unitary regulators to put forward a framework for finite, alternative quantum theories to a given quantum field theory. Feynman-like rules of such a finite, alternative quantum theory lead to alternative, perturbative Green functions. Which are acceptably regularized perturbative expansions of the original Green functions, causal, and imply no unphysical free particles. To demonstrate that the proposed framework is feasible, we take the quantum field theory of a single, self-interacting real scalar field and show how we can alter, covariantly and locally, its free-field Lagrangian to obtain finite, alternative perturbative Green functions.