Abstract

In this paper we extend the bosonic D-brane action in D = 10 obtained by duality from the D = 11 membrane wrapped on S-1 to an SU(2)non- Abelian system. This system presents only first class constraints, whose algebra closes off-shell and generalizes the algebra of diffeomorphisms of the D2 brane to include non- Abelian symmetry generators. From theSU( 2) D- brane action, we also obtain the SU( 2) Born - Infeld theory by performing a covariant reduction to a flat background. This calculation agrees up to fourth order with the result obtained from the superstring amplitudes and gives an alternative approach to analyse non- Abelian Born - Infeld theories.