The Dynamics of Relativistic Membranes II: Nonlinear Waves and Covariantly Reduced Membrane Equations

Abstract

By explicitly eliminating all gauge degrees of freedom in the $3+1$-gauge description of a classical relativistic (open) membrane moving in $\Real^3$ 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 Poincaré 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 Poincaré-invariant nonlinear wave-equation. This approach also gives a simple derivation of the nonlinear gas dynamic equation obtained in the light-cone gauge.

10 pages, LATEX, FR-THEP-93-19 and KA-THEP-5-93

References in corpus (4)

• The Dynamics of Relativistic Membranes I: Reduction to 2-dimensional Fluid Dynamics
• Universal Field Equations with Covariant Solutions D.B. Fairlie
• Universal Field Equations with Reparametrisation Invariance
• Linearisation of Universal Field Equations

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