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

摘要

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