  Two different gauge potential methods are engaged to calculate explicitly the
spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit
interaction is expressed in terms of kinematic momenta by introducing a gauge
potential. A formulation of the spin Hall conductivity is established by
requiring that the time evolution of this kinematic momentum vector vanishes.
We then calculated the conductivity employing the Berry gauge fields. We show
that both of the gauge fields can be deduced from the pure gauge field arising
from the Foldy-Wouthuysen transformations.
