Related papers: New length operator for loop quantum gravity

The Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of…

This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…

We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…

We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is…

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well-defined on the Hilbert space ( H_Poly ). It is henceforth deemed impossible to define…

In special relativity theory the physical quantities are generally expressed as function of the velocity. In the particular case of an extended object, the factor 1/gamma of Lorentz contraction of its length in the direction of motion is…

This paper establishes several new inequalities for the $A$-norm and $A$-numerical radius of operator sums in semi-Hilbertian spaces, significantly advancing the existing theory. We present two fundamental refinements of the generalized…

We show that for basically all states, the evolution of the expectation value of the volume operator in Wheeler-DeWitt and various homogenous isotropic loop quantum comology (LQC) models ($k=0$, coupled to massless scalar field and without…

The loop quantization of Brans-Dicke theory (with coupling parameter $\omega\neq-3/2$) is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity…

We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…

The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…

We consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity. First we introduce correlation functions with geodesic distances between operators kept fixed. Next by making two of the…

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…

We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…

We start with the Hamiltonian formulation of the first order action of pure gravity with a full $\mathfrak{sl}(2,\mathbb C)$ internal gauge symmetry. We make a partial gauge-fixing which reduces $\mathfrak{sl}(2,\mathbb C)$ to its…

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity programme, and is…

Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…

There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the…