Related papers: Gravitational null rays: Covariant Quantization an…
In a sense of deformation quantization, noncommutative (NC) geometry introduces a quantum structure of spacetime. Using the twist-deformation formalism, we show that the dynamical effects of spacetime noncommutativity can amount to a…
Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes von Neumann…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
The paper contains a complete theory of factors for ray representations acting in a Hilbert bundle, which is a generalization of the known Bargmann's theory. With the help of it we have reformulated the standard quantum theory such that the…
The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…
In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in Loop Quantum Gravity (LQG). In one spatial…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…
This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schr\"odinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing,…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
A common feature of the extended phase space of gauge theory, the crossed product of quantum theory, and quantum reference frames (QRFs) is the adjoining of degrees of freedom followed by a constraining procedure for the resulting total…
In quantum gravity, physically meaningful operator is required to be invariant under the diffeomorphisms. Such gauge invariant operator is typically given by the relational observable, the operator localized in relation to some background…
All physical observations are made relative to a reference frame, which is a system in its own right. If the system of interest admits a group symmetry, the reference frame observing it must transform commensurately under the group to…
Recent work [hep-th/0504183,hep-th/0508002] indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets twisted and…
We present a non-perturbative quantization of gravitational null initial data. Our starting point is the characteristic null initial problem for tetradic gravity with a parity-odd Holst term in the bulk. After a basic review about the…
We develop a non-linear distributional renormalisation algebra for Gaussian Quantum Foam, built from sequences of scaled Gaussians on spacelike hypersurfaces of homotopic, globally hyperbolic spacetimes and their distributional limits. The…
This paper considers the problem of consistently defining subsystems in gravitational theories. It is argued that a subsystem is a spacetime subregion in which the observables form a closed Poisson algebra. In a generally covariant theory,…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this…
We study Heisenberg's uncertainty relation relative to a quantum reference frame (QRF). We introduce the QRF as a covariant phase-space observable, show that when described relative to it, position and momentum appear compatible, and derive…