Atomic levels in superstrong magnetic fields and D=2 QED of massive electrons: screening

TL;DR

This paper investigates how superstrong magnetic fields cause photon mass generation and Coulomb potential screening, revealing differences from 2D QED and implications for hydrogen atom energy at extreme fields.

Contribution

It demonstrates the qualitative difference in screening behavior between 3D superstrong magnetic fields and 2D QED, and calculates the finite ground state energy of hydrogen under these conditions.

Findings

Photon polarization induces a dynamical photon mass leading to Coulomb screening.

Screening behavior differs qualitatively from D=2 QED, affecting potential at different distances.

Hydrogen atom ground state energy becomes finite at ultra-strong magnetic fields.

Abstract

The photon polarization operator in superstrong magnetic fields induces the dynamical photon "mass" which leads to screening of Coulomb potential at small distances $z\ll 1/m$, $m$ is the mass of an electron. We demonstrate that this behaviour is qualitatively different from the case of D=2 QED, where the same formula for a polarization operator leads to screening at large distances as well. Because of screening the ground state energy of the hydrogen atom at the magnetic fields $B \gg m^2/e^3$ has the finite value $E_0 = -me^4/2 \ln^2(1/e^6)$.