  Ginzburg-Landau (GL) equations and GL free energy for flux phase and
superconductivity are derived microscopically from the $t-J$ model on a square
lattice. Order parameter (OP) for the flux phase has direct coupling to a
magnetic field, in contrast to the superconducting OP which has minimal
coupling to a vector potential. Therefore, when the flux phase OP has
unidirectional spatial variation, staggered currents would flow in a
perpendicular direction. The derived GL theory can be used for various problems
in high-$T_c$ cuprate superconductors, e.g., states near a surface or
impurities, and the effect of an external magnetic field. Since the GL theory
derived microscopically directly reflects the electronic structure of the
system, e.g., the shape of the Fermi surface that changes with doping, it can
provide more useful information than that from phenomenological GL theories.
