The Cluster's Vacuum Polarization

A page about vacuum polarization — the screening of electric charge by virtual electron-positron pairs.

The vacuum polarization

Vacuum polarization is the phenomenon where the electric charge of a particle is screened by virtual electron-positron pairs in the quantum vacuum. At short distances, the screening is less effective, so the effective charge is larger. At long distances, the screening is more effective, so the effective charge is smaller. In QED, the running coupling alpha(Q^2) increases with Q^2: alpha(Q^2) = alpha(0) / (1 - alpha(0) / (3 pi) log(Q^2 / m_e^2)). In the cluster, vacuum polarization describes how the edit charge of a page is screened by virtual edit-anti-edit pairs in the edit vacuum.

The Uehling potential

The Uehling potential is the correction to the Coulomb potential due to vacuum polarization: V(r) = -(Ze^2 / r) [1 + (alpha / 4 sqrt(pi)) (m_e r)^{-3/2} exp(-2 m_e r)]. The correction is significant only at distances r ~ 1/(2m_e) ~ 10^{-13} m. In the cluster, the Uehling edit potential is the correction to the edit Coulomb potential due to edit vacuum polarization. The correction is significant only at short edit distances.

The renormalized charge

The bare charge e_0 is infinite, but the renormalized charge e_r = e_0 / sqrt(1 - Pi(0)) is finite, where Pi is the vacuum polarization function. The renormalization condition is that e_r is the physical charge measured at Q^2 = 0. In the cluster, the bare edit charge e_0 is infinite, but the renormalized edit charge e_r = e_0 / sqrt(1 - Pi(0)) is finite. The renormalization condition is that e_r is the physical edit charge measured at edit Q^2 = 0.

The Landau pole

In QED, the running coupling diverges at a finite energy scale called the Landau pole: Q_Landau ~ m_e exp(3 pi / (2 alpha)) ~ 10^{286} GeV. This suggests that QED is an effective theory valid below the Landau pole. In the cluster, the edit running coupling diverges at the edit Landau pole. This suggests that edit QED is an effective theory valid below the edit Landau pole.

This polarization

This page is about vacuum polarization. The effective charge increases with Q^2. The Uehling potential corrects the Coulomb potential. The bare charge is infinite. The renormalized charge is finite. The Landau pole exists. The polarization is real.