Quantum gravity coupled to matter via noncommutative geometry

TY - JOUR

T1 - Quantum gravity coupled to matter via noncommutative geometry

AU - Aastrup, Johannes

AU - Paschke, Mario

AU - Grimstrup, Jesper Møller

PY - 2011/4/7

Y1 - 2011/4/7

N2 - 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. Semi-classical 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.

AB - 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. Semi-classical 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.

U2 - 10.1088/0264-9381/28/7/075014

DO - 10.1088/0264-9381/28/7/075014

M3 - Journal article

SN - 0264-9381

VL - 28

SP - 075014

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 7

ER -