Related papers: Comments on area spectra in Loop Quantum Gravity
We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular…
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy…
The precise analog of the theta-quantization ambiguity of Yang-Mills theory exists for the real SU(2) connection formulation of general relativity. As in the former case theta labels representations of large gauge transformations, which are…
After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In…
Area metrics and area metric backgrounds provide a unified framework for quantum gravity. They encode physical degrees of freedom beyond those of a metric. These non-metric degrees of freedom must be suppressed by a potential at…
The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended…
Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But a number of their features remain elusive. The best studied one -the euclidean Barrett-Crane model- does not have the boundary state space…
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$…
The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of Loop Quantum Gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that…
We introduce squeezed vacua in loop quantum gravity, a new overcomplete basis of states that contain prescribable correlations between geometric operators. We study the behavior of long-range correlations and discuss the relevance of these…
In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In…
We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function…
In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with…
Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened…
We apply a singularity resolution technique utilized in loop quantum gravity to the polymer representation of quantum mechanics on R with the singular -1/|x| potential. On an equispaced lattice, the resulting eigenvalue problem is identical…
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports,…
The spectrum of triangular band matrices defined on the sequence spaces where the entries of each band is a constant or convergent sequence is well studied. In this article, the spectrum and fine spectrum of a new generalised difference…
In ``On restricting to one-loop order the radiative effects in quantum gravity" (Brandt, Frenkel, and McKeon, 2020) \cite{Brandt2020}, a Lagrange multiplier (LM) field is introduced into the Einstein-Hilbert action, removing all multi-loop…