  Non-trivial configurations of Yang-Mills fields and gravitational backgrounds
induce charges on Dp-branes that couple them to lower and higher RR potentials.
We show that these couplings can be described in a systematic and coordinate
independent way by using Clifford multiplication. In the minimal formulation,
D-brane charges and RR potentials combine into bispinors of an SO(1,9) which is
defined with a flat metric and does not coincide with the space-time Lorentz
group. In a non-minimal formulation, the RR potentials combine into SO(10,10)
spinors while the space of charges is formally enlarged to construct SO(10,10)
bispinors. The formalism suggests that the general form of the gravitational
contribution to the D-brane charges is not modified, though the replacement of
wedge product by Clifford multiplication gives rise to new couplings,
consistent with T-duality.
