  In this work, the Ginzburg-Landau theory is represented on a symplectic
manifold with a phase space content. The order parameter is defined by a
quasi-probability amplitude, which gives rise to a quasi-probability
distribution function, i.e., a Wigner-type function. The starting point is the
thermal group representation of Euclidean symmetries and gauge symmetry.
Well-known basic results on the behavior of a superconductor are re-derived,
providing the consistency of representation. The critical superconducting
current density is determined and its usual behavior is inferred. The
negativety factor associated with the quasi-distribution function is analyzed,
providing information about the non-classicality nature of the superconductor
state in the region closest to the edge of the superconducting material.
