Properties of the Eleven-Dimensional Supermembrane Theory

We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N=8 world volume (rigid) supersymmetry in a “physical� gauge; we also present the field equations and transformation rules in a “lightcone� gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowki)4 × (flat 7-torus), and review some mathematical results that are relevant for path integral quantization