THE DYNAMICS OF RELATIVISTIC MEMBRANES .2. NONLINEAR-WAVES AND COVARIANTLY REDUCED MEMBRANE EQUATIONS

By explicitly eliminating all gauge degrees of freedom in the 3 + 1-gauge description of a classical relativistic (open) membrane moving in R3 We derive a 2 + 1-dimensional nonlinear wave equation of Born-Infeld type for the graph z(t, x, y) which is invariant under the Poincare group in four dimensions. Alternatively, we determine the world-volume of a membrane in a covariant way by the zeroes of a scalar field u(t, x, y, z) obeying a homogeneous Poincare-invariant nonlinear wave-equation. This approach also gives a simple derivation of the nonlinear gas dynamic equation obtained in the light-cone gauge.