E7(7) on the light cone

We use the Cremmer-Julia E7(7) non-linear symmetry of N = 8 Supergravity to derive its order κ2 on-shell Hamiltonian in terms of one chiral light-cone superfield. By requiring that E7(7) commute with the super-Poincare group, we deduce to lowest non-trivial order in κ, the light cone E7(7) transformations of all fields of the theory, including the graviton. We then derive the dynamical supersymmetry transformation to order κ2, and express the Hamiltonian as a quadratic form in the chiral superfield.