  The construction of a $covariant$ Loop Wave functional equation in a 4D
spacetime is attained by introducing a generalized $eleven$ dimensional
categorical {\bf C}-space comprised of $8\times 8$ antisymmetric matrices. The
latter matrices encode the generalized coordinates of the histories of points,
loops and surfaces $combined$. Spacetime Topology change and the Holographic
principle are natural consequences of imposing the principle of $covariance$ in
{\bf C}-space. The Planck length is introduced as a necessary rescaling
parameter to establish the correspondence limit with the physics of
point-histories in ordinary Minkowski space, in the limit $l_P\to 0$. Spacetime
quantization should appear in discrete units of Planck length, area, volume
,....All this seems to suggest that the generalized principle of covariance,
representing invariance of proper $area$ intervals in {\bf C}-space, under
matrix-coordinate transformations, could be relevant in discovering the
underlying principle behind the origins of $M$ theory. We construct an ansatz
for the $SU(\infty)$ Yang-Mills vacuum wavefunctional as a solution of the
Schroedinger Loop Wave equation associated with the Loop Quantum Mechanical
formulation of the Eguchi-Schild String . The Strings/Loops ($SU(\infty)$ gauge
field) correspondence implements one form of the Bulk/Boundary duality
conjecture in this case.
