  We show how the partition function of a network of parallel superconducting
wires weakly coupled together by the proximity effect, subjected a vector
potential along the wires can be mapped onto N-distinguishable two dimensional
quantum-mechanics problem with a perpendicular imaginary magnetic field. Then,
we show, using a mean field approximation, that, for a given coupling, there is
a critical temperature for onset of inter-wire phase coherence. The transition
temperature $T_c$ is plotted on both cases for non-magnetic and a magnetic
field perpendicular to the wires.
