Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity

We show that 10D spinor helicity formalism can be understood as spinor moving frame approach to supersymmetric particles extended to the description of amplitudes. This allows us to develop the spinor helicity formalism for 11D supergravity and a new constrained superfield formalism for 10D SYM and 11D SUGRA amplitudes. We show how the constrained on-shell superfields, one-particle counterparts of the superamplitudes, can be obtained by quantization of massless superparticle mechanics. We make some stages towards the calculation of amplitudes of 10D SYM and 11D SUGRA in this framework. In particular we have found supersymmetric Ward identities for constrained amplitudes and an especially convenient gauge, fixed on the spinor frame variables corresponding to scattered particles, which promises to be an extremely useful tool for further development of our approach. We also discuss a candidate for generalization of the BCFW recurrent relations for the constrained tree superamplitudes, indicate and discuss a problem of dependence of the expressions obtained with it on a deformation vector, which is not fixed uniquely in higher dimensional $D>4$ cases.