Related papers: Modular Theory, Non-Commutative Geometry and Quant…
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all…
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes…
We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of…
We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and…
We discuss how Moyal deformations of gauge theories, which arise naturally from open string theory, fit into the paradigm of colour-kinematics duality and the double copy of gauge theory to gravity. Along the way we encounter novel…
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
An important object appearing in the framework of the Tomita--Takesaki theory is an invariant cone under the modular automorphism group of von Neumann algebras. As a result of the connection between von Neumann algebras and quantum field…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
I review recent progress in understanding non-perturbative aspects of string theory, quantum gravity and non-commutative geometry using lattice methods.
We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of quantum principal bundles and noncommutative complex…
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads…