相关论文: What kind of noncommutative geometry for quantum g…

We introduce a framework for non-linear time evolution in quantum mechanics as a natural non-linear generalization of the Schrodinger equation. Within our framework, we derive simple toy models of dynamical geometry on finite graphs. Along…

These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…

The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…

The progress of noncommutative geometry has been crucially influenced, from the beginning, by quantum physics: we review this development in recent years. The Standard Model, with its central role for the Dirac operator, led to several…

We present a short review describing the use of noncommutative space-time in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their…

Spacetime manifolds that are not time orientable play a key role in a gravitational explanation of quantum theory. Such manifolds allow topology change, but also have fascinating additional properties such as net charge from source-free…

This thesis is devoted to studying various aspects of quantum mechanics on non-commutative space-time and to capture some of the surviving aspects of symmetries of quantum field theory on such space-time, illustrated through toy models in…

Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the…

We briefly discuss some possible cosmological implications of noncommutative geometry. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of other fields that are present in the…

We give a brief non-technical introduction to non-regular spacetime geometry. In particular, we discuss how curvature, and hence gravity, can be defined without a smooth (differential geometric) calculus.

The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…

General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…

Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…

An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time…

The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to…

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…

Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…

In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…

A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An…

The restrictions imposed on the strong force in the `non-commutative standard model' are examined. It is concluded that given the framework of non-commutative geometry and assuming the electroweak sector of the standard model many details…