  Magnetic field lines are quantum objects carrying one quantum
$\Phi_0=2\pi\hbar/e$ of magnetic flux and have finite radius $\lambda_m$. Here
we argue that they possess a very specific dynamical interaction. Parallel
field lines reject each other. When confined to a certain area they form
two-dimensional lattices of hexagonal structure. We estimate the filling factor
of such an area. Antiparallel field lines, on the other hand, attract each
other. We identify the physical mechanism as being due to the action of the
gauge potential field which we determine quantum mechanically for two parallel
and two antiparallel field lines. The distortion of the quantum electrodynamic
vacuum causes a cloud of virtual pairs. We calculate the virtual pair
production rate from quantum electrodynamics and estimate the virtual pair
cloud density, pair current and Lorentz force density acting on the field lines
via the pair cloud. These properties of field line dynamics become important in
collisionless reconnection, consistently explaining why and how reconnection
can spontaneously set on in the field-free centre of a current sheet below the
electron-inertial scale.
