M. Bordemann et J. Hoppe, THE DYNAMICS OF RELATIVISTIC MEMBRANES .2. NONLINEAR-WAVES AND COVARIANTLY REDUCED MEMBRANE EQUATIONS, Physics letters. Section B, 325(3-4), 1994, pp. 359-365
By explicitly eliminating all gauge degrees of freedom in the 3 + 1-ga
uge description of a classical relativistic (open) membrane moving in
R3 We derive a 2 + 1-dimensional nonlinear wave equation of Born-Infel
d 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-equa
tion. This approach also gives a simple derivation of the nonlinear ga
s dynamic equation obtained in the light-cone gauge.