Related papers: New volume and inverse volume operators for loop q…
We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual)…
Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop…
In a previous article we have introduced an operator representing the three-dimensional scalar curvature in loop quantum gravity. In this article we examine the new curvature operator in the setting of quantum-reduced loop gravity. We…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…
We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to…
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…
A previous paper constructed a kinematic basis for spin networks with planar or cylindrical symmetry and arbitrary polarization. This paper imposes a constraint which limits the gravitational wave to a single polarization. The spectrum of…
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
2+1 gravity coupled to a massless scalar field has an initial singularity when the spatial slices are compact. The quantized model is used here to investigate several issues of quantum gravity. The spectrum of the volume operator is studied…
Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements…
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…
The aim of this letter is to indicate the differences between the Rovelli-Smolin quantum volume operator and other quantum volume operators existing in the literature. The formulas for the operators are written in a unifying notation of the…
Within the context of loop quantum gravity there are several operators which measure geometry quantities. This work examines two of these operators, volume and angle, to study quantum geometry at a single spin network vertex - ``an atom of…
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…