Reconnection occurs as a result of the breakdown of the frozen-in theorem. This theorem basically states that the flux of the magnetic field through a closed loop moving with the fluid is conserved. This allows one to think of the magnetic field lines as
Particles which are initially connected by a field line This is true only when one assumes infinite conductivity. This is generally not the case for a plasma, in which there exists a finite resistance. This can be stated mathematically using Ohm's law along with Faraday's and Ampére's laws.
The derivation is simply substituting E from Ohm's law and J from Ampére's law into Faraday's Law. The resulting equation is:
where which is the resistivity. If the term involving is neglected then the field lines will remain connected indefinitely. However, when non-negligible resistance develops, as in the diffusion region, this term is no longer small enough, and very large-scale changes can occur.