  The light-cone Hamiltonians for spin 1 and spin 2 fields, describing both the
pure and the maximally supersymmetric theories, may be expressed as quadratic
forms. In this paper, we show that this feature extends to light-cone higher
spin theories. To first order in the coupling constant, we prove that the
higher spin Hamiltonians, with and without supersymmetry, are quadratic forms.
Scattering amplitude structures emerge naturally in this framework and we
relate the momentum space vertex in a supersymmetric higher spin theory to the
corresponding vertex in the N=4 Yang-Mills theory.
