  The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge
in a semi-classical approximation from a abstract spectral triple construction.
The spectral triple is constructed over an algebra of holonomy loops,
corresponding to a configuration space of connections, and encodes information
of the kinematics of General Relativity. The emergence of the Dirac Hamiltonian
follows from the observation that the algebra of loops comes with a dependency
on a choice of base-point. The elimination of this dependency entails spinor
fields and, in the semi-classical approximation, the structure of the Dirac
Hamiltonian.
