On mass-dependent subtraction and removal of the ambiguity in QED renormalization

TL;DR

This paper introduces a mass-dependent subtraction scheme for QED renormalization at a time-like point, ensuring gauge invariance, Lorentz invariance, and convergence, leading to unambiguous, physically consistent results and explicit expressions for effective parameters.

Contribution

It presents a novel mass-dependent subtraction method for QED renormalization that removes ambiguities and maintains physical symmetries, with explicit solutions for effective parameters.

Findings

Renormalized results are free of ambiguity and respect physical symmetries.

Explicit expressions for effective coupling and mass are valid across all distances.

The scheme allows expressing S-matrix elements similarly to tree diagrams with effective parameters.

Abstract

The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge symmetry, the Lorentz- invariance and the mathematical convergence. Therefore, the renormalized results derived in the subtraction scheme are faithful and have no ambiguity. Especially, it is proved that the solution of the renormalization group equation satisfied by a renormalized wave function, propagator or vertex can be fixed by applying the renormalization boundary condition and of the form as given in the Feynman rules and, thus, an exact S-matrix element can be expressed in the form as written in the tree diagram approximation provided that the coupling constant and the fermion mass are replaced by their effective ones. In the one-loop approximation, the effective coupling constant and the effective fermion mass obtained by solving their renormalization group equations are given in rigorous and explicit expressions which are suitable in the whole range of distance. and exhibit physically reasonable asymptotic behaviors.