The wave-particle duality in the Weyl-Dirac theory

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: B-c2, 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.