New look at the modified Coulomb potential in a strong magnetic field

Abstract

The static Coulomb potential of Quantum Electrodynamics (QED) is calculated in the presence of a strong magnetic field in the lowest Landau level (LLL) approximation using two different methods. First, the vacuum expectation value of the corresponding Wilson loop is calculated perturbatively in two different regimes of dynamical mass m dyn. , i.e., |q 2 | ≪ m 2 dyn. ≪ |eB| and m 2 dyn. ≪ |q 2 | ≪ |eB|, where q is the longitudinal components of the momentum relative to the external magnetic field B. The result is then compared with the static potential arising from Born approximation. Both results coincide. Although the arising potentials show different behavior in the aforementioned regimes, a novel dependence on the angle θ between the particle-antiparticle's axis and the direction of the magnetic field is observed. In the regime |q 2 | ≪ m 2 dyn. ≪ |eB|, for strong enough magnetic field and depending on the angle θ, a qualitative change occurs in the Coulomb-like potential; Whereas for θ = 0, π the potential is repulsive, it exhibits a minimum for angles θ ∈]0, π[.

Critical nucleus charge in a superstrong magnetic field

“…The Dirac equation for electron both in an external magnetic field and in the Coulomb field of a nucleus was numerically solved in [6]. The exact solutions of [6] were compared with the approximate analytical ones of [5] (see (9)) in Figures 1 and 2 in [6].…”

“…For the ground level at ε > 0 one should take n = 0, while for ε < 0 it should be changed to n = −1. According to (9) when the magnetic field increases the ground state energy goes down and reaches the lower continuum. The value of the magnetic field at which this happens is determined by the formula:…”

“…For example, in an external magnetic field vacuum polarization in one loop is strongly enhanced and proportional to magnetic field strength B. It was discovered by Shabad and Usov [7,8] (see also [9]) that this enhancement leads to the significant modification (screening) of the Coulomb potential for B m 2 /e 3 where m and e are electron mass and charge 1 . The potential was found numerically along the magnetic field on the line going through the charge and in the direction transverse to the magnetic field in the plane containing the charge.…”

Modified Coulomb potential of QED in a strong magnetic field

“…Recently, this potential is calculated in [3] and [1]. In [3], it is shown that the standard Coulomb law is modified by the vacuum polarization arising in the external magnetic field.…”

“…In these proceedings, after briefly introducing QED in an external magnetic field, we will present the results from [1], where this potential is determined anew by computing perturbatively the vacuum expectation value (VEV) of the corresponding Wilson loop to a static fermion-antifermion pair. In the regime of LLL dominance, two different regions of dynamical mass m dyn.…”