  A study of the one loop dilatation operator in the scalar sector of $\cal N$
$=$ 4 SYM is presented. The dilatation operator is analyzed from the point of
view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in
the planar large $N$ limit is presented, and its role in understanding the
integrability of the planar dilatation operator is emphasized. A classical
limit of the dilatation operator is obtained by considering a contraction of
this Lie algebra, leading to a new way of constructing classical limits for
quantum spin chains. An infinite tower of local conserved charges is
constructed in this classical limit purely within the context of the matrix
model. The deformation of these charges and their relation to the charges of
the spin chain is also elaborated upon.
