相关论文: Eigenvalues of the volume operator in loop quantum…

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…

The volume operator is an important kinematical quantity in the non-perturbative approach to four-dimensional quantum gravity in the connection formulation. We give a general algorithm for computing its spectrum when acting on four-valent…

In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…

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…

The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general…

We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…

The search for a quantum theory of gravity is one of the major challenges facing theoretical physics today. While no complete theory exists, a promising avenue of research is the loop quantum gravity approach. In this approach, 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,…

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 spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…

To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In the series of papers, we will introduce a graphical method, developed by Yutsis and Brink, to loop…

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…

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,…

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…

We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…

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…

Loop Quantum Gravity is the major candidate of quantum gravity. It is interesting to consider its continuum limit, which corresponds to the classical limit. We consider the Gaussian weave state, which describes a semi-classical picture. We…

We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on…

We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat…