Tachyonic decay of unstable Dirichlet branes

We consider an unstable bound system of two supersymmetric Dirichlet branes of different dimensionality ($p,p'$ with $p'<p$) embedded in a flat non-compactified IIA or IIB type background. We study the decay, via tachyonic condensation, of such unstable bound states leading to a pair of bound D$(p-1)$, D$p'$-branes. We show that only when the gauge fields carried by the D$p$-brane are localised perependicular to the tachyon direction, then tachyon condensation will indeed take place. We perform our analysis by combining both, the Hamiltonian and the Lagrangian approach.