Real-polynomial formulation of general relativity in terms of connections

I show in this Brief Report that it is possible to construct a Hamiltonian description for Lorentzian general relativity in terms of two real SO(3) connections. The constraints are simple polynomials in the basic variables. The present framework gives us a new formulation of general relativity that keeps some of the interesting features of the Ashtekar formulation without the complications associated with the complex character of the latter.