Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 super-particle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = closed integral lambda(alpha) d(alpha) where d(alpha) is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and lambda(alpha) is an SO(10, 1) pure spinor variable satisfying lambdaGamma(c) lambda = 0 for c = 1 to 11. Super-Poincare covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = Q(L) + Q(R) is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, lambdaGamma(11) lambda = 0, replaces the b(L)(0) - b(R)(0) constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators.