We obtain forms of Born-Infeld and D-brane actions that are quadratic in derivatives of X and linear in F-mu nu by introducing an auxiliary 'metric' which has both symmetric and anti-symmetric parts, generalising the simplification of the Nambu-Goto action for p-branes using a symmetric metric. The abelian gauge field appears as a Lagrange multiplier, and solving the constraint gives the dual form of the n dimensional action with an n - 3 form gauge field instead of a vector gauge field. We construct the dual action explicitly, including cases which could not be covered previously. The generalisation to supersymmetric D-brane actions with local fermionic symmetry is also discussed. (C) 1997 Elsevier Science B.V.
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