On the Dirac-Born-Infeld Action for D-branes

In this note, we consider the reformulation of the Dirac-Born-Infeld action for a Dirichlet p-brane in Brink-Di Vecchia-Howe-Tucker form, i.e., including an independent non-propagating world-volume metric. When p>2, the action becomes non-polynomial. A closed expression is derived for p=3. For selfdual field-strengths, the DBI action is reproduced by an action with a simple F^2 term. We speculate on supersymmetrization of the D_3-brane action. We also give the governing equations for arbitrary p, and derive an implicit expression for the D_4-brane lagrangian.