Gauge Invariance and Hall Terms in the Quasiclassical Equations of Superconductivity

This paper presents a careful derivation of the quasiclassical equations of superconductivity so that a manifest gauge invariance is retained with respect to the space-time arguments of the quasiclassical Green's function $\hat{g}$. The terms responsible for the Hall effect naturally appear from the derivation. The equations are applicable to clean as well as dirty superconductors for an arbitrary external frequency much smaller than the Fermi energy. Thus, they will form a basis toward a complete microscopic understanding of the Hall effect in type-II superconductors.