Quantum gravity coupled to matter via noncommutative geometry

Johannes Aastrup (1) , Jesper Møller Grimstrup (2) , Mario Paschke (3)

1 Mathematisches Institut
2 NBI - Niels Bohr Institute [Copenhagen]
3 Spaß & Wissenschaft

We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a configuration space of connections. It involves an algebra of holonomy loops represented as bounded operators on a separable Hilbert space and a Dirac type operator. Semiclassical states, which involve an averaging over points at which the product between loops is defined, are constructed and it is shown that the Dirac Hamiltonian emerges as the expectation value of the Dirac type operator on these states in a semi-classical approximation.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Johannes Aastrup, Jesper Møller Grimstrup, Mario Paschke. Quantum gravity coupled to matter via noncommutative geometry. Classical and Quantum Gravity, 2011, 28 (7), pp.75014. ⟨10.1088/0264-9381/28/7/075014⟩. ⟨hal-00686095⟩