Non-renormalizable theories and finite formulation of QFT

TL;DR

This paper extends the finite formulation of quantum field theory to non-renormalizable theories, enabling divergence-free calculations of effective actions and correlation functions, demonstrated with a scalar field example.

Contribution

It introduces a generalized finite formulation for non-renormalizable QFTs using Callan-Symanzik equations, allowing divergence-free computations.

Findings

Explicit finite calculations of effective potential and correlation functions.

No quantum corrections to scalar mass depending on the scale M^2.

Method applicable to arbitrary scalar field theories.

Abstract

In this paper, we show how the finite formulation of QFT based on Callan-Symanzik equations can be generalised to the case of non-renormalizable theories. We derive an equation for effective action for an arbitrary single scalar field theory, allowing us to perform computations without running in intermediate divergencies. We illustrate the method with the use of $\lambda\phi^4 + \phi^6/M^2$ theory by the explicit (and fully finite) calculations of the effective potential as well as two-, four- and six-point correlation functions at one loop level and demonstrate that no quantum corrections to scalar mass $m^2$, depending on $M^2$-scale, are generated.