  We propose a macroscopic description of the superconducting state in presence
of an applied external magnetic field in terms of first order differential
equations. They describe a corrugated two-component order parameter intertwined
with a spin-charged background, caused by spin correlations and charged
dislocations. The first order differential equations are a consequence of a
Weitzenb\"ock-Liechnorowitz identity which renders a SUL(2) \otimes UL(1)
invariant ground state, based on (L) local rotational and electromagnetic gauge
symmetry. The proposal is based on a long ago developed formalism by \'Elie
Cartan to investigate curved spaces, viewed as a collection of small Euclidean
granules that are translated and rotated with respect to each other. \'Elie
Cartan's formalism unveils the principle of local rotational invariance as a
gauge symmetry because the global SU(2) invariance of the order parameter is
turned local by the interlacement of spin and charge to pairing.
