A new Hamiltonian structure for general relativity

A new form of the dynamical equations of vacuum general relativity is proposed. This form involves a new Hamiltonian structure and non canonical variables. The new field variables are the electric field E and the magnetic field of A from the Ashtekar representation of the (complex) gravitational phase space. The Poisson brackets between functionals of the field, which emerge from this framework, are compatible with the constraints satisfied by the field variables. The quantization is briefly outlined