Magneticfieldlinesarequantumobjectscarrying onequantum0=2πh ̄/eofmagneticfluxandhavefinite radius λm. Here we argue that they possess a very specific dynamicalinteraction.Parallelfieldlinesrejecteachother. When confined to a certain area they form two-dimensional lattices of hexagonal structure. We estimate the filling factor of such an area. Anti-parallel field lines, on the other hand, at- tract each other. We identify the physical mechanism as being due to the action of the gauge potential field, which we de- termine quantum mechanically for two parallel and two anti- parallel field lines. The distortion of the quantum electrody- namic vacuum causes a cloud of virtual pairs. We calculate the virtual pair production rate from quantum electrodynam- ics 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 im- portant 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.
Treumann, R A.; Baumjohann, W; and Gonzalez, W. D., "Collisionless reconnection: magnetic field line interaction" (2012). Open Dartmouth: Faculty Open Access Articles. 435.