On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
Abstract
The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge in a semiclassical 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 basepoint. The elimination of this dependency entails spinor fields and, in the semiclassical approximation, the structure of the Dirac Hamiltonian.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.3802
 Bibcode:
 2010arXiv1003.3802A
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, two figures.