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.