Lagrange brackets and U(1) fields

The idea of a companion Lagrangian associated with p-branes is extended to include the presence of U(1) fields. The brane Lagrangians are constructed with Fij represented in terms of Lagrange brackets, which make manifest the reparametrisation invariance of the theory; these are replaced by Poisson brackets in the companion Lagrangian, which is now covariant under field redefinition. The ensuing Lagrangians possess a similar formal structure to those in the absence of an anti-symmetric field tensor.