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

The static Coulomb potential of quantum electrodynamics (QED) is calculated in the presence of a strong magnetic field in the lowest Landau level 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(parallel to)(2)\<< m(dyn)(2)<<\eB\ and m(dyn)(2)<<\q(parallel to)(2)\<<\eB\, where q(parallel to) is the longitudinal component 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 theta between the particle-antiparticle's axis and the direction of the magnetic field is observed. In the regime \q(parallel to)(2)\<< m(dyn)(2)<<\eB\, for strong enough magnetic field and depending on the angle theta, a qualitative change occurs in the Coulomb-like potential; whereas for theta=0, pi the potential is repulsive, it exhibits a minimum for angles theta is an element of]0,pi[.