# Quantum holonomy theory

@article{Aastrup2015QuantumHT, title={Quantum holonomy theory}, author={Johannes Aastrup and Jesper M{\o}ller Grimstrup}, journal={Protein Science}, year={2015}, volume={64}, pages={783-818} }

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 holonomy-diffeomorphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical… Expand

#### 11 Citations

A ug 2 02 0 The Metric Nature of Matter

- 2020

We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved… Expand

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

- 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… Expand

The Metric Nature of Matter

- Physics, Mathematics
- 2020

We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved… Expand

On Representations of the Quantum Holonomy Diffeomorphism Algebra

- Mathematics, Chemistry
- Fortschritte der Physik
- 2019

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… Expand

On nonperturbative quantum field theory and noncommutative geometry

- Mathematics, Physics
- Journal of Geometry and Physics
- 2019

A general framework of non-perturbative quantum field theory on a curved background is presented. A quantum field theory is in this setting characterised by an embedding of a space of field… Expand

M ay 2 01 6 Quantum Holonomy Theory and Hilbert Space Representations

- 2018

We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of… Expand

On the Fermionic Sector of Quantum Holonomy Theory

- Mathematics, Physics
- 2018

In this paper we continue the development of quantum holonomy theory, which is a candidate for a fundamental theory based on gauge fields and non-commutative geometry. The theory is build around the… Expand

Quantum Gravity and the Emergence of Matter

- Physics, Mathematics
- 2017

In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which… Expand

2 1 A pr 2 01 6 Quantum Holonomy Theory and Hilbert Space Representations

- 2016

We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of… Expand

On a Lattice-Independent Formulation of Quantum Holonomy Theory

- Physics, Mathematics
- 2016

Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M) algebra, which essentially encodes how matter degrees of… Expand

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