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The inter-particle 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 will be studied for large Euclidean time. The resulting
potential will then be compared with the potential arising from a
semi-classical Born approximation. It shows different behavior in
two regimes of dynamical mass, $ |{\mathbf{q}}_{\|}^{2}|\ll
m_{dyn.}^{2}\ll |eB|$ and $m_{dyn.}^{2}\ll
|\mathbf{q}_{\|}^{2}|\ll|eB|$, where $\mathbf{q}_{\|}$ is the
longitudinal components of the momentum relative to the external
magnetic field $B$. A novel dependence of the potential on the angle
$\theta$ between the particle-antiparticle's axis and the direction
of the magnetic field is observed. We will show that in the first
regime $|{\mathbf{q}}_{\|}^{2}|\ll m_{dyn.}^{2}\ll |eB|$ for large
enough magnetic field, bound states can be formed for
$\theta\in]0,\pi[$.
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