  The quantum mechanical transition between a free particle Lagrangian and the
Klein Gordon field description of a free particle (particle wave duality) is
conjectured to extend to an analogous construction of relativistically
invariant wave equations associated with strings and branes, which we propose
to call brane-wave duality. Electromagnetic interactions in the two systems are
discussed. It is emphasised that all integrable free field theories, including
those of Dirac-Born-Infeld type, are associated with Lagrangians equivalent to
divergences on the space of solutions of the equations of motion.
