Holonomy loops, spectral triples and quantum gravity

TY - JOUR

T1 - Holonomy loops, spectral triples and quantum gravity

AU - Johannes , Aastrup

AU - Grimstrup, Jesper Møller

AU - Nest, Ryszard

N1 - Based on talks given by Jesper Møller Grimstrup at the QG2 Conference, Nottingham, July 2008; at the QSTNG Conference in Rome in Sept/Oct 2008; at the AONCG Conference, Canberra, Dec 2008.

PY - 2009/7/27

Y1 - 2009/7/27

N2 - We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac-type operator resembles a global functional derivation operator and the interaction between the algebra of holonomy loops and the Dirac-type operator reproduces the structure of a quantized Poisson bracket of general relativity. Finally, we give a heuristic argument as to how a natural candidate for a quantized Hamiltonian might emerge from this spectral triple construction

AB - We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac-type operator resembles a global functional derivation operator and the interaction between the algebra of holonomy loops and the Dirac-type operator reproduces the structure of a quantized Poisson bracket of general relativity. Finally, we give a heuristic argument as to how a natural candidate for a quantized Hamiltonian might emerge from this spectral triple construction

U2 - 10.1088/0264-9381/26/16/165001

DO - 10.1088/0264-9381/26/16/165001

M3 - Journal article

SN - 0264-9381

SP - 165001

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

ER -