相关论文: Discreteness of area and volume in quantum gravity

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…

We show how the spectrum of normal discrete short-range infinite-volume operators can be approximated with two-sided error control using only data from finite-sized local patches. As a corollary, we prove the computability of the spectrum…

We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which a $SU(2)$ connection is diagonal and it is therefore surprising that the operator…

We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a "minimum-area principle". We show that an…

We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of…

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…

In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero…

The aim of this article is to provide a rigorous-but-simple steps to prove the hermiticity of the volume operator of Rovelli-Smolin and Ashtekar-Lewandowski using the angular momentum approach, as well as pointing out some subleties which…

Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms…

A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to…

Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also…

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…

I argue that the prediction of physical discreteness at the Planck scale in loop gravity is a reasonable conclusion that derives from a sensible ensemble of hypotheses, in spite of some contrary arguments considered in an interesting recent…

We investigate the quantum area operator in the loop approach based on the Lorentz covariant hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines…

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…

A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…

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…

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…

In this article, we study the quantum theory of gravitational boundary modes on a null surface. These boundary modes are given by a spinor and a spinor-valued two-form, which enter the gravitational boundary term for self-dual gravity.…

The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…