Covariant canonical formalism for Dirac-Nambu-Goto bosonic p-branes and the Gauss-Bonnet topological term in string theory

Using a covariant and gauge invariant geometric structure constructed on the Witten covariant phase space for Dirac-Nambu-Goto bosonic p-branes propagating in a curved background, we find the canonically conjugate variables, and the relevant commutation relations are considered, as well as, we find the canonical variables for the Gauss-Bonnet topological term in string theory.