Non-abelian Born-Infeld action

We introduce a realization of the algebra of diffeomorfisms in terms of the fields of a non-abelian Born-Infeld theory(NBI), which generalizes the abelian case. We argue that the non-abelian Born Infeld action which describes the interaction of D-branes in the low energy regime, may be constructed from the Hamiltonian obtained by taking the symmetry generators as gauge constraints. We explicitly obtain the interacting terms to the sixth order in the curvature of the Yang-Mills fields. Our results for the NBI action agree up to the fourth order with the ones obtained from the interacting string theory.