  We present an extension of the Courant bracket to the ones for Dp-branes by
analyzing Hamiltonians and local superalgebras. Contrast to the basis of the
bracket for a fundamental string which consists of the momentum and the winding
modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show
that the R-R gauge transformation rules are obtained by these Courant brackets
for Dp-branes where the Dirac-Born-Infeld gauge field and the "two-vierbein
field" play an essential role. Canonical analysis of the worldvolume theories
naturally gives the basis of the brackets and the target space backgrounds
keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis
S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the
R-R coupling.

High Energy Physics - Theory