Hamiltonian Formulation of the Supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the Hamiltonian formalism is developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given by two approaches: The first is Dirac approach where the covariant is splited into primary and secondary class constraints is exhibited, and their Dirac brackets are constructed. The second is Guler Approach, (Hamilton-Jacobi) in which the equations of motion are obtained as total differenial equations in many variables without the need to distinguish between primary and secondary constraints. These equations of motion are in exact agreement with those equations that had been obtained using Dirac’s method