  We present the construction of a physical Hamiltonian operator in the
deparametrized model of loop quantum gravity coupled to a free scalar field.
This construction is based on the use of the recently introduced curvature
operator, and on the idea of so-called "special loops". We discuss in detail
the regularization procedure and the assignment of the loops, along with the
properties of the resulting operator. We compute the action of the squared
Hamiltonian operator on spin network states, and close with some comments and
outlooks.
