  By replacing ten-dimensional pure spinors with eleven-dimensional pure
spinors, the formalism recently developed for covariantly quantizing the d=10
superparticle 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=int (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 (lambda Gamma^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, (lambda Gamma^{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.
