  We report a simplification in the large N matrix mechanics of light-cone
matrix field theories. The absence of pure creation or pure annihilation terms
in the Hamiltonian formulation of these theories allows us to find their
reduced large N Hamiltonians as explicit functions of the generators of the
Cuntz algebra. This opens up a free-algebraic playground of new reduced models
-- all of which exhibit new hidden conserved quantities at large N and all of
whose eigenvalue problems are surprisingly simple. The basic tool we develop
for the study of these models is the infinite dimensional algebra of all
normal-ordered products of Cuntz operators, and this algebra also leads us to a
special number-conserving subset of these models, each of which exhibits an
infinite number of new hidden conserved quantities at large N.
