2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56226The 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.14 pages, latex, no figures. Clarification of the type of Lagrangians used; references addedHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext