On spectral triples in quantum gravity. II.

DOI10.4171/JNCG/30zbMath1158.46312arXiv0802.1784MaRDI QIDQ960531

Johannes Aastrup, Ryszard Nest, Jesper Møller Grimstrup

Publication date: 22 December 2008

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1784

zbMATH Keywords

noncommutative geometryDirac operatorslattice gauge theoryspaces of connectionsholonomy loopssemifinite spectral triples

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Quantization of the gravitational field (83C45) Noncommutative geometry methods in quantum field theory (81T75) Methods of noncommutative geometry in general relativity (83C65) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Noncommutative geometry (à la Connes) (58B34)

Related Items (12)

On Representations of the Quantum Holonomy Diffeomorphism Algebra ⋮ \(C^\ast\)-algebras of holonomy-diffeomorphisms \& quantum gravity. II ⋮ The JLO character for the noncommutative space of connections of Aastrup-Grimstrup-Nest ⋮ On semi-classical states of quantum gravity and noncommutative geometry ⋮ Spectral action for a one-parameter family of Dirac operators on $\bm{ SU}\textbf {(2)}$SU(2) and $\bm{SU}\textbf {(3)}$SU(3) ⋮ Quantum lattice gauge fields and groupoid \(\mathrm{C}^{\ast}\)-algebras ⋮ On inductive limit spectral triples ⋮ Quantum holonomy theory ⋮ ON THE JLO COCYCLE AND ITS TRANSGRESSION IN ENTIRE CYCLIC COHOMOLOGY ⋮ A new spectral triple over a space of connections ⋮ On nonperturbative quantum field theory and noncommutative geometry ⋮ QUANTIZATION OF THE G-CONNECTIONS VIA THE TANGENT GROUPOID

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