## About

46

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931

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Introduction

Education

September 1999 - August 2002

April 1998 - May 1999

## Publications

Publications (46)

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 configurations into a Hilbert space over R ∞. This embedding, which is only local up to a scale that we interpret as the Planck scale, coincides in the local an...

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 algebra, which is an algebra generated by holonomy‐diffeomorphisms and by translation operators on an underlying configuration space of connections, exist. We construct ope...

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 is an algebra generated by holonomy-diffeomorphisms and by translation operators on an underlying configuration space of Ashtekar connections, exist....

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 holonomy-diffeomorphisms on a 3-manifold
and a quantized Dirac type operator; the two capturing the kinematics of
quantum gravity formulated in terms of Ashtek...

We introduce the holonomy-diffeomorphism algebra, a C*-algebra generated by
flows of vectorfields and the compactly supported smooth functions on a
manifold. We show that the separable representations of the
holonomy-diffeomorphism algebra are given by measurable connections, and that
the unitary equivalence of the representations corresponds to me...

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 QHD(M) algebra, which is generated by parallel transports along flows of vector fields and translation operators on an underlying configuration space o...

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 configurations into a Hilbert space over $\mathbb{R}^\infty$. This embedding, which is only local up to a scale that we interpret as the Planck scale, coincides...

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 freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensio...

Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD-algebra, which essentially encodes how local degrees of freedom are moved on a three-dimensional manifold. In this paper we continue the development of the theory by providing a lattice-independent formulation....

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 v...

We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we sho...

We review applications of noncommutative geometry in canonical quantum
gravity. First, we show that the framework of loop quantum gravity includes
natural noncommutative structures which have, hitherto, not been explored.
Next, we present the construction of a spectral triple over an algebra of
holonomy loops. The spectral triple, which encodes the...

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 general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is k...

The quantization of the noncommutative , U(1) super-Yang–Mills action is performed in the superfield formalism. We calculate the one-loop corrections to the self-energy of the vector superfield. Although the power-counting theorem predicts quadratic ultraviolet and infrared divergences, there are actually only logarithmic UV and IR divergences, whi...

We discuss the different possibilities of constructing the various energy–momentum tensors for noncommutative gauge field models. We use Jackiw's method in order to get symmetric and gauge invariant stress tensors — at least for commutative gauge field theories. The noncommutative counterparts are analyzed with the same methods. The issues for the...

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 semi-classical states are constructed which,
in a semi-classical limit, give a system of interacting fermions in an ambient
gravitational field. The interaction...

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 spectral triple gives the Dirac Hamiltonian in 3+1
dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our an...

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 sepa...

The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge in a semi-classical approximation from a abstract spectral triple construction. The spectral triple is constructed over an algebra of holonomy loops, corresponding to a configuration space of connections, and encodes information of the kinematics of General Relativity. The...

We present a separable version of Loop Quantum Gravity (LQG) based on an inductive system of cubic lattices. We construct semi-classical states for which the LQG operators -- the flux, the area and the volume operators -- have the right classical limits. Also, we present the Hamilton and diffeomorphism constraints as operator constraints and show t...

We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foli...

A new construction of a semifinite spectral triple on an algebra of holonomy loops is presented. The construction is canonically
associated to quantum gravity and is an alternative version of the spectral triple presented in [1].

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 fun...

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 subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two pape...

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the al...

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 general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is...

The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops
closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of Lie-groups
composed of copies of the gauge group. A spectral triple over the space of connections is obtained by...

We construct covariant coordinate transformations on the
fuzzy sphere and utilize these to construct a covariant map from a
gauge theory on the fuzzy sphere to a gauge theory on the ordinary
sphere. We show that this construction coincides with the
Seiberg-Witten map on the Moyal plane in the appropriate limit. The
analysis takes place in the algeb...

Noncommutative conformal transformations are constructed on noncommutative {R}4 and used to derive the Seiberg-Witten differential equation.

We analyse two new versions of -expanded non-commutative quantum electrodynamics up to first order in and first loop order. In the first version we expand the bosonic sector using the Seiberg-Witten map, leaving the fermions
unexpanded. In the second version we leave both bosons and fermions unexpanded. The analysis shows that the Seiberg-Witten
ma...

In this letter we apply the methods of our previous paper, hep-th/0108045, to noncommutative fermions. We show that the fermions
form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations into a field-dependent
part and a -part implies the Seiberg-Witten differential equations for the fermions.

We discuss the algebraic construction of topological models (of both
Schwarz- and Witten-type) within the Batalin-Vilkovisky formalism and we
elaborate on a simple description of vector supersymmetry within this
framework.

We discuss $\theta$-deformed Maxwell theory at first order in $\theta$ with the help of the Seiberg-Witten (SW) map. With an appropriate field redefinition consistent with the SW-map we analyse the one-loop corrections of the vacuum polarization of photons. We show that the radiative corrections obtained in a previous work may be described by the W...

We analyse the IR singularities that appear in a noncommutative
scalar quantum field theory. We demonstrate, with the help of the
effective action and an appropriate field redefinition, that no
IR singularities appear in the quadratic part at one-loop order.
No new degrees of freedom are needed to describe the UV/IR mixing.

We show that the noncommutative Yang-Mills field forms an irreducible
representation of the (undeformed) Lie algebra of rigid translations, rotations
and dilatations. The noncommutative Yang-Mills action is invariant under
combined conformal transformations of the Yang-Mills field and of the
noncommutativity parameter \theta. The Seiberg-Witten dif...

We show that the photon self-energy in quantum
electrodynamics on noncommutative 4 is renormalizable to
all orders (both in θ and ) when using the
Seiberg-Witten map. This is due to the enormous freedom in the
Seiberg-Witten map which represents field redefinitions and generates
all those gauge invariant terms in the θ-deformed classical
action whi...

With the help of the Seiberg-Witten map for photons and fermions we define a theta-deformed QED at the classical level. Two possibilities of gauge-fixing are discussed. A possible non-Abelian extension for a pure theta-deformed Yang-Mills theory is also presented.

We investigate the quantization of the theta-expanded noncommutative U(1) Yang-Mills action, obtained via the Seiberg-Witten map. As expected we find non-renormalizable terms. The one-loop propagator corrections are gauge independent, and lead us to a unique extention of the noncommutative classical action. We interpret our results as a requirement...

We present the discussion of the energy-momentum tensor of the scalar $\phi^4$- theory on a noncommutative space. The Noether procedure is performed at the operator level. Additionally, the broken dilatation symmetry will be considered in a Moyal-Weyl deformed scalar field theory at the classical level.

We introduce the notion of superoperators on non-commutative R 4 and re-investigate in the framework of superfields the non-commutative Wess-Zumino model as a quantum field theory. In a highly efficient manner we are able to confirm the result that this model is renormalizable to all orders.

We introduce the notion of superoperators on noncommutative R^4 and re-investigate in the framework of superfields the noncommutative Wess-Zumino model as a quantum field theory. In a highly efficient manner we are able to confirm the result that this model is renormalizable to all orders. Comment: 17 pages, 4 figures, LaTeX, minor changes, referen...

A U(N) Chern-Simons theory on non-commutative R-3 is constructed as a theta -deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and theta -independent at the one-loop level and that the calculations respect the restriction of t...

We present a simple derivation of vector supersymmetry
transformations for topological field theories of Schwarz- and
Witten-type. Our method is similar to the derivation of
BRST-transformations from the so-called horizontality conditions or
russian formulae. We show that this procedure reproduces in a concise
way the known vector supersymmetry tra...

A new topological model is proposed in three dimensions as an extension of the BF-model. It is a three-dimensional counterpart of the two-dimensional model introduced by Chamseddine and Wyler ten years ago. The BFK-model, as we shall call it, shows to be quantum scale invariant at all orders in perturbation theory. The proof of its full finiteness...

## Questions

Question (1)

Together with my colleague Johannes Aastrup I have launched a crowdfunding campaign

in order to seek out alternative funding for our research.

It has been our experience that a project like ours, which is far off the mainstream research directions (in our case: String Theory and Loop Quantum Gravity), is very hard to fund through the ordinary funding agencies. So we decided to try something completely different.

Can this work? The answers appears to be YES. So far we've got almost 250 backers and + 25.000$.