The solution of a static two-dimensional wave equation in the
Gauss-Mainardi-Codazzi formalism of Weyl-Dirac theory is obtained in
terms of the elliptic function with a complex argument. In particular, by
double degenerating the elliptic function, wave-particle duality
results. Associating a superconducting behaviour to matter, by means of
the duality, we find some superconducting parameters: Bc2, the
average
carrier density, the gap energy and the pair-breaking time. The
discontinuities of these parameters for sequences (1/3),
(1/5), (1/7),... imply
that the quantum spacetime is Cantorian.