Related papers: The complete spectrum of the area from recoupling …
We summarize the basics of the loop representation of quantum gravity and describe the main aspects of the formalism, including its latest developments, in a reorganized and consistent form. Recoupling theory, in its graphical…
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…
We present a straightforward and self-contained introduction to the basics of the loop approach to quantum gravity, and a derivation of what is arguably its key result, namely the spectral analysis of the area operator. We also discuss the…
I discuss the role played by the spin-network basis and recoupling theory (in its graphical tangle-theoretic formulation) and their use for performing explicit calculations in loop quantum gravity. In particular, I show that recoupling…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We study the distribution of the eigenvalues of the area operator in loop quantum gravity concentrating on the part of the spectrum relevant for isolated horizons. We first show that the approximations relying on integer partitions are not…
We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum…
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite,…
The lowest 37000 eigenvalues of the area operator in loop quantum gravity is calculated and studied numerically. We obtain an asymptotical formula for the eigenvalues as a function of their sequential number. The multiplicity of the lowest…
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…
Loop quantum gravity admits a kind of area quantization that is characterized by three quantum numbers. We show the complete spectrum of area is the union of equidistant subsets and a universal reformulation with fewer parameters is…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of…
In this note we show that in a two-dimensional non-commutative space the area operator is quantized, this outcome is compared with the result obtained by Loop Quantum Gravity methods.
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,…
We introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. The operator is constructed by writing the Ricci scalar classically as a function of the Ashtekar variables and regularizing the…
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…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…
Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the…