A four-dimensional approach to quantum field theories

TL;DR

This paper introduces a novel four-dimensional regularization method (FDR) for quantum field theories that handles ultraviolet divergences without traditional renormalization, maintaining gauge invariance and simplifying the treatment of infinities.

Contribution

The paper presents the FDR approach, a new four-dimensional integral method that reabsorbs divergences into vacuum expectations, avoiding the need for UV regulators and preserving gauge invariance.

Findings

FDR reproduces the ABJ anomaly correctly.

FDR is independent of UV regulators.

FDR can regularize infrared and collinear divergences.

Abstract

I present a novel Four-Dimensional Regularization/Renormalization approach (FDR) to ultraviolet divergences in field theories which can be interpreted as a natural separation between physical and non physical degrees of freedom. Based on the observation that some infinities can be reabsorbed into the vacuum expectation value of the fields, rather than into the parameters of the Lagrangian, a new type of four-dimensional loop integral is introduced (the FDR integral) which is independent of any UV regulator and respects all properties required by gauge invariance. FDR reproduces the correct ABJ anomaly and no change in the definition of gamma_5 is needed. With FDR the possibility is open for an approach to UV infinities in which the renormalization program is substituted by a simple reinterpretation of the appearing loop integrals as FDR ones, leading to important consequences in the context of non-renormalizable field theories. Finally, I show how FDR can also be used to regularize infrared and collinear divergences.