Reformulation Instead of Renormalizations

TL;DR

This paper proposes a reformulation of quantum field theory that avoids renormalization by focusing on the correct variable choice, simplifying calculations of fundamental constants and physical effects.

Contribution

It introduces a classical analogy to demonstrate how variable choice impacts perturbative corrections, leading to a new formulation of QFT without renormalizations.

Findings

Avoids infrared and ultraviolet problems in QED scattering

Simplifies calculations of Lamb shift and magnetic moments

Eliminates the need for renormalization procedures

Abstract

In this article I show why the fundamental constants obtain perturbative corrections in higher orders, why the renormalizations work and how to reformulate the theory in order to avoid these technical and conceptual complications. I demonstrate that the perturbative mass and charge corrections are caused exclusively with the kinetic nature of the interaction Lagrangian. As soon as it is not purely quantum mechanical (or QFT) specific feature, the problem can be demonstrated on a classical two-body problem. The latter can be solved in different ways, one of them being correct and good for applying the perturbation theory (if necessary) and another one being tricky and awkward. The first one is physically and technically natural - it is a center-of-inertia-and-relative-variable formulation. The second one - mixed variable formulation - is unnecessarily complicated and leads to the mass and charge corrections even in the Newtonian mechanics of two bound bodies. The perturbation theory in QFT is factually formulated in the mixed variables - that is why it brings corrections to the fundamental constants. This understanding opens a way of correctly formulating the QFT equations and thus to simplify the QFT calculations technically and conceptually. For example, in scattering problems in QED it means accounting exactly the quantized electromagnetic field influence in the free in and out states of charged particles so no infrared and ultraviolet problems arise. In bound states it means obtaining the energy corrections (the Lamb shift, the anomalous magnetic moment) quite straightforwardly and without renormalizations.