E7(7) invariant Lagrangian of d=4 N=8 supergravity

We present an E-7(7) invariant Lagrangian that leads to the equations of motion of d = 4 N = 8 supergravity without using Lagrange multipliers. The superinvariance of this new action and the closure of the supersymmetry algebra are proved explicitly for the terms that differ from the Cremmer-Julia formulation. Since the diffeomorphism symmetry is not realized in the standard way on the vector fields, we switch to the Hamiltonian formulation in order to prove the invariance of the E-7(7) invariant action under general coordinate transformations. We also construct the conserved E-7(7)-Noether current of maximal supergravity and we conclude with comments on the implications of this manifest off-shell E-7(7)-symmetry for quantizing d = 4 N = 8 supergravity, in particular on the E-7(7)-action on phase space.