# Intersecting Quantum Gravity with Noncommutative Geometry { a Review ?

@article{Aastrup2012IntersectingQG, title={Intersecting Quantum Gravity with Noncommutative Geometry \{ a Review ?}, author={Johannes Aastrup and Jesper M{\o}ller Grimstrup}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2012}, volume={8}, pages={018} }

We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural non- commutative structures which have, hitherto, not been explored. Next, we present the con- struction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the…

## Figures from this paper

## 14 Citations

On nonperturbative quantum field theory and noncommutative geometry

- Physics, MathematicsJournal of Geometry and Physics
- 2019

Quantum holonomy theory

- Mathematics, Physics
- 2015

We present quantum holonomy theory, which is a non‐perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C* ‐algebra that involves…

C*-algebras of holonomy-diffeomorphisms and quantum gravity: I

- Mathematics
- 2013

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local…

Aspects of noncommutative spectral geometry

- Physics
- 2017

This thesis presents aspects of noncommutative spectral geometry as an approach to formulate a model of gravity and particle physics, while addressing open issues associated with this approach. We…

M ay 2 02 0 Representations of the Quantum Holonomy-Diffeomorphism Algebra

- Mathematics
- 2020

In this paper we continue the development of Quantum Holonomy Theory, which is a candidate for a fundamental theory, by constructing separable strongly continuous representations of its algebraic…

Quantum Lattice Gauge Fields and Groupoid C∗-Algebras

- Mathematics
- 2019

We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C∗-algebras to describe the observables. We introduce direct systems…

Proton decay and the quantum structure of space–time

- PhysicsCanadian Journal of Physics
- 2019

Virtual black holes in noncommutative space–time are investigated using coordinate coherent state formalism such that the event horizon of a black hole is manipulated by smearing it with a Gaussian…

The Gribov problem in noncommutative QED

- Mathematics, Physics
- 2015

A bstractIt is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of…

Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity

- Physics, Mathematics
- 2014

Connes' formula defines a distance in loop quantum gravity, via the spinfoam Dirac operator. A simple notion of spectral distance on a graph can be extended do the discrete Lorentzian context,…

## References

SHOWING 1-10 OF 66 REFERENCES

INTERSECTING CONNES NONCOMMUTATIVE GEOMETRY WITH QUANTUM GRAVITY

- Mathematics
- 2007

An intersection of noncommutative geometry and loop quantum gravity is proposed. Alain Connes' noncommutative geometry provides a framework in which the Standard Model of particle physics coupled to…

On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

- Mathematics
- 2011

We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the…

Quantum gravity coupled to matter via noncommutative geometry

- Mathematics
- 2011

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…

From Quantum Gravity to Quantum Field Theory via Noncommutative Geometry

- Physics
- 2011

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity…

Holonomy Loops, Spectral Triples & Quantum Gravity

- Mathematics
- 2009

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…

Non-commutative fermion mass matrix and gravity

- Physics
- 2013

The first part is an introductory description of a small cross-section of the literature on algebraic methods in nonperturbative quantum gravity with a specific focus on viewing algebra as a…

Gravity coupled with matter and the foundation of non-commutative geometry

- Mathematics
- 1996

We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds. Its unitary representations correspond…

On spectral triples in quantum gravity II

- Mathematics
- 2009

A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric…

Quantum Gravity (Cambridge Monographs on Mathematical Physics)

- Physics
- 2005

The most difficult unsolved problem in fundamental theoretical physics is the consistent implementation of the gravitational interaction into a quantum framework, which would lead to a theory of…