相关论文: Counting surface states in the loop quantum gravit…

Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…

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…

The geometric operators of area, volume, and length, depend on a fundamental length l of quantum geometry which is a priori arbitrary rather than equal to the Planck length l_P. The fundamental length l and the Immirzi parameter $\gamma$…

We review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of…

A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large…

Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…

We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…

In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or {\em punctures}) labelled by spin $j$. The excitations possibly carry other internal degrees of freedom…

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…

In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the…

Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.

The issue of black hole entropy is reexamined within a finite lattice framework along the lines of Wheeler, 't Hooft and Susskind, with an additional criterion to identify physical horizon states contributing to the entropy. As a…

Entanglement entropy quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this…

Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…

The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…

We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states…

It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…

The entropy of apparent horizons is derived using coherent states or semiclassical states in quantum gravity. The leading term is proportional to area for large horizons, and the correction terms differ according to the details of the graph…

The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is…

In the framework of loop quantum gravity (LQG), having quantum black holes in mind, we generalize the previous boundary state counting (gr-qc/0508085) to a full bulk state counting. After a suitable gauge fixing we are able to compute the…