Puzzles of Divergence and Renormalization in Quantum Field Theory

TL;DR

This paper introduces a regularization renormalization method ($RRM$) in quantum field theory that simplifies calculations by avoiding divergences, counterterms, and arbitrary scales, and applies it to various fundamental problems.

Contribution

The paper proposes a novel $RRM$ approach that streamlines quantum field theory calculations without explicit divergences or counterterms, and demonstrates its application to key QFT issues.

Findings

Calculations are unambiguous with no explicit divergences.

Applicable to Lamb shift, running coupling constants, and Higgs mass.

Method simplifies QFT renormalization without arbitrary scales.

Abstract

A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times, rendering it just convergent. Then integrate it back into $I$ with some arbitrary constants appeared. Third, the renormalization is nothing but a process of reconfirmation to fix relevant parameters (mass, charge, \etc) by experimental data via suitable choices of these constants. Various $QFT$ problems, including the Lamb shift, the running coupling constants in $QED$ and $QCD$, the $\lambda \phi^4$ model as well as Higgs mass in the standard model of particle physics, are discussed. Hence the calculation, though still approximate and limited in accuracy, can be performed in an unambiguous way with no explicit divergence, no counter term, no bare parameter and no arbitrarily running mass scale (like the $\mu$ in $QCD$).