  Microscopically, collisionless reconnection in thin current sheets is argued
to involve `composite electrons' in the ion inertial (Hall current) domain, a
tiny fraction of electrons only. These `composite electrons' are confined to
lower Landau levels $\epsilon_L\ll T_e$ (energy much less than temperature).
They demagnetise by absorbing magnetic flux quanta $\Phi_0=h/e$, decouple from
the magnetic field, transport the attached magnetic flux into the non-magnetic
centre of the current layer, where they release the flux in the form of
micro-scale magnetic vortices, becoming ordinary electrons. The newly born
micro-scale magnetic vortices reconnect in their strictly anti-parallel
sections when contacting other vortices, ultimately producing the meso-scale
reconnection structure. We clarify the notions of magnetic field lines and
field line radius, estimate the power released when two oppositely directed
flux quanta annihilate, and calculate the number density and Landau-level
filling-factor of `composite electrons' in the Hall domain. As side product we
find that the magnetic diffusion coefficient in plasma also appears in quanta
$D_0^m=e\Phi_0/m_e=h/m_e$, yielding that the bulk perpendicular plasma
resistivity is quantised, with quantum (lowest limit) $\eta_{\,0\perp}=\mu_0
e\Phi_0/m_e=\mu_0h/m_e\sim 10^{-9}$ Ohm m.
  Keywords: Reconnection, thin current sheets, quantum Hall effect, quantised
diffusivity, quantised plasma resistivity, composite electrons
