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 D3-brane action. We also give the governing equations for arbitrary p, and derive an implicit expression for the D4-brane lagrangian.