Running couplings from adiabatic regularization

Antonio Ferreiro,Jose Navarro-Salas

doi:10.1016/j.physletb.2019.03.026

Abstract

We extend the adiabatic regularization method by introducing an arbitrary mass scale μ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding μ-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.

Highlights

Quantum field theories are intrinsically plagued with ultraviolet divergences, which need to be first isolated with the help of a regularization method and removed to produce finite results. This is the so-called renormalization procedure, which was developed to prove the perturbative consistency of quantum electrodynamics (QED) and led to very significant predictions, like the anomalous magnetic moment of the electron
Another remarkable prediction is the effective running of the electric charge, tied to vacuum polarization phenomena
Demanding that the bare electric charge be independent of the renormalization scale μ leads to the effective running of the electric charge in QED: e2(μ2)

Summary

Running couplings from adiabatic regularization

Antonio Ferreiro1, ∗ and Jose Navarro-Salas1, † 1Departamento de Fısica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC. Facultad de Fısica, Universidad de Valencia, Burjassot-46100, Valencia, Spain. We extend the adiabatic regularization method by introducing an arbitrary mass scale μ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding μ-invariance of the effective semiclassical (Maxwell-Einstein) equations. We get the running of the electric charge of perturbative quantum electrodynamics. The method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization

INTRODUCTION

General covariance strongly restricts the way one could

The semiclassical

Fσρ σρ gαβ

CONCLUSIONS AND FINAL COMMENTS