The observable-state model and non-renormalizable theories

TL;DR

This paper applies the observable-state model to n quantum field theories, demonstrating finite correlation functions and deriving renormalization group equations without counterterms, thus offering a novel approach to non-renormalizable theories.

Contribution

It introduces a method to obtain finite correlation functions and renormalization group equations in n theories without counterterms, expanding the applicability of the observable-state model.

Findings

Finite 2-point and n-point correlation functions achieved without counterterms.

Derived renormalization group equations for mass and coupling constant.

Explored the validity of the observable-state model via the projection procedure.

Abstract

The aim of this work is to apply the observable-state model for the quantum field theory of a \phi^n self- interaction. We show how to obtain finite values for the 2-point and n-point correlation functions without introducing counterterms in the Lagrangian. Also, we show how to obtain the renormalization group equation for the mass and the coupling constant. Finally, we found the dependence of the coupling constant with the energy scale and we discuss the validity of the observable-state model in terms of the projection procedure.