Fermions in quantum gravity

The quantum fermions plus gravity system (QGD) is studied using the loop representation. A Hamiltonian is constructed that governs the evolution in the physical time given by a (``clock'') scalar field. The Hamiltonian, defined via a regularization, is finite, background independent, and diffeomorphism invariant; it acts on intersections and end points of open curves. The dynamics is thus coded into combinatorics of graphs (``topological Feynman rules''). Exact dynamical states are exhibited. Surprisingly the fermion dynamics is the immediate extension of pure gravity dynamics to open loops.