Some physical implications of the Weyl-Dirac theory

The solution of a wave equation in the Gauss-Mainardi-Codazzi formalism of Weyl-Dirac theory is obtained in terms of the elliptic function. In particular, by degenerating the elliptic function, plane-wave, wavepacket, kink and soliton results. Each particular solution corresponds to certain values of the curvature scaler and of the cosmological constant, so chat the entity manifests different wave-particle properties in different geometric situations. Associating a superconducting behaviour to matter, by means of the kink solution, we find the dependences on the reduced temperature of the superconducting parameters, in other words, we develop a thermodynamics of the isolated particle. Using the soliton solution we show char for any particle we can define a particular waveguide.