New N=4 supersymmetric Yang-Mills path integral

Using Lorentz-covariant spinor helicity formalism, we reorganize the unitary scalar superfield light-cone path integral for the N = 4 supersymmetric Yang-Mills theory. In new variables in the chiral Fourier superspace, the quadratic and cubic parts of the classical action have manifest Lorentz, kinematical and dynamical supersymmetry, with the exception of terms which contribute only to the contact terms in the supergraphs with propagators shrinking to a point. These terms have the same structure as supergraphs with quartic light-cone vertices, which break dynamical supersymmetry. We present evidence that all complicated terms breaking dynamical supersymmetry have to cancel and therefore can be omitted. It is plausible that the new form of the path integral leads to a set of relatively simple unitarity based rules with manifest N = 4 supersymmetry.