Related papers: Intersecting Quantum Gravity with Noncommutative G…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
It has been known for some time now that error correction plays a fundamental role in the determining the emergence of semiclassical geometry in quantum gravity. In this work I connect several different lines of reasoning to argue that this…
We apply one of the formalisms of noncommutative geometry to $R^N_q$, the quantum space covariant under the quantum group $SO_q(N)$. Over $R^N_q$ there are two $SO_q(N)$-covariant differential calculi. For each we find a frame, a metric and…
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…
We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that…
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields…
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative…
We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…