相关论文: Counting surface states in the loop quantum gravit…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of geometry of quantum type I…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
We propose that any compact $d$-manifold with elliptic data, $\mathcal{J}$, prepares a quantum state $|\mathcal{J}\rangle$ on its $(d-1)$-boundary $\sigma$. Elliptic data consists of metric and field values, or their conjugates, but not…
We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to…
A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area…
Open quantum systems interacting with the environments often show interesting behaviors, such as decoherence, non-unitary evolution, dissipation, etc. It is interesting but still challenging to study the open quantum gravitation system…
Without imposing the trapping boundary conditions and only from within the very definition of area it is shown that the loop quantization of area manifests an unexpected degeneracy in area eigenvalues. This could lead to a deeper…
We introduce simple generic models of surface dynamics in loop quantum gravity (LQG). A quantum surface is defined as a set of elementary patches of area glued together. We provide it with an extra structure of locality (nearest neighbors),…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically…
The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total…
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions. The state counting problem effectively reduces to the well studied…
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…
The precise analog of the theta-quantization ambiguity of Yang-Mills theory exists for the real SU(2) connection formulation of general relativity. As in the former case theta labels representations of large gauge transformations, which are…
Gravity is a macroscopic manifestation of a microscopic quantum theory of space-time, just as the theories of elasticity and hydrodynamics are the macroscopic manifestation of the underlying quantum theory of atoms. The connection of…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…