Related papers: Comments on Non-Commutative Phenomenology
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
We question the notion of line element in some quantum spaces that are expected to play a role in quantum gravity, namely non-commutative deformations of Minkowski spaces. We recall how the implementation of the Leibniz rule forbids to see…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
We investigate topology-changing processes in 4-dimensional quantum gravity with a negative cosmological constant. By playing the ``gluing-polytope game" in hyperbolic geometry, we explicitly construct an instanton-like solution without…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
We discuss two scenarios of emergent gravity. In one of them the quantum vacuum is considered as superplastic crystal, and the effective gravity describes the dynamical elastic deformations of this crystal. In the other one the…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
We study a family of noncommutative spacetimes constructed by one four-vector. The large set of coordinate commutation relations described in this way includes many cases that are widely studied in the literature. The Hopf-algebra…
We consider a class of models with infinite extra dimension, where bulk space does not possess SO(1,3) invariance, but Lorentz invariance emerges as an approximate symmetry of the low-energy effective theory. In these models, the maximum…
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We…
This paper follows recent steps towards a nonassociative quantum theory and points out the mathematical structure behind the proposed modifications to conventional quantum theory. An N=1 supersymmetry model and a strong force glueball…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…
3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
Noncommutative three-dimensional gravity can be described in terms of a noncommutative Chern-Simons theory. We extend this structure and also propose an action for gravitational fields on an even dimensional noncommutative space. The action…
We discuss the role that interactions play in the non-commutative structure that arises when the relative coordinates of two interacting particles are projected onto the lowest Landau level. It is shown that the interactions in general…