Semiclassical states in loop quantum gravity: an introduction

Unifying general relativity and quantum mechanics is a great challenge left to us by Einstein. To face this challenge, considerable progress has been made in non-perturbative canonical (loop) quantum gravity during the past 20 years. The kinematical Hilbert space of the quantum theory is constructed rigorously. However, the semiclassical analysis of the theory is still a crucial and open issue. In this review, we first introduce our work on constructing a semiclassical weave state, using the [ω] operator on the kinematical Hilbert space of loop quantum gravity. Then we give an introduction to the two different approaches currently investigated for constructing coherent states in the kinematical Hilbert space. The current status of semiclassical analysis in loop quantum gravity is then summarized.     

Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

用圈量子引力解除Schwarichild-de Sitter黑洞的时空奇点

通过引入圈量子引力中holonomy基本变量的类比变量和采用相应的量子化方法,对Schwarichild-de Sitter黑洞中心附近的引力场进行量子化.分析和计算了黑洞中心附近的1r和曲率标量的谱分布,得到了它们均存在有限上界的结果.通过求解经典时空奇点r=0附近的量子哈密顿约束方程,给出了黑洞波函数在黑洞中心附近的时间演化行为,得到了该波函数可以通过经典奇点进行量子演化的结果.     

Canonical quantum gravity and consistent discretizations

This paper covers some developments in canonical quantum gravity that occurred since ICGC-2000, emphasizing the recently introduced consistent discretizations of general relativity.     

Loop quantum gravity and black hole entropy quantization

Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity, the minimum horizon area gap is obtained. Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization. The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi. Supported by the National Natural Science Foundation of China (Grant No. 10773002)     

Fermions in three-dimensional spinfoam quantum gravity

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition amplitude of the theory. The path integral is derived as a sum over closed fermionic loops wrapping around the spinfoam. The effects of quantum torsion are realised as a modification of the intertwining operators assigned to the edges of the two-complex, in accordance with loop quantum gravity. The creation of non-trivial curvature is modelled by a modification of the pure gravity vertex amplitudes. The appendix contains a review of the geometrical and algebraic structures underlying the classical coupling of fermions to three dimensional gravity.     

Radiative effects and dimension 5 operators arising from quantum gravity

We examine radiative corrections arising from Lorentz violating dimension five operators presumably associated with Planck scale physics as recently considered by Myers and Pospelov. We find that observational data result in bounds on the dimensionless parameters of the order 10^–15. These represent the most stringent bounds on Lorentz violation to date.     

On the interaction of mesoscopic quantum systems with gravity

We review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non‐relativistic expansions of the Klein‐Gordon and Dirac equations in the post‐Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated.     

Problem of time in quantum gravity

The Problem of Time occurs because the ‘time’ of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the very early universe. Emphasis in this Review is on the Problem of Time being multi‐faceted and on the nature of each of the eight principal facets. Namely, the Frozen Formalism Problem, Configurational Relationalism Problem (formerly Sandwich Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time, Problem of Beables (alias Problem of Observables) and Spacetime Reconstruction/Replacement Problem. Strategizing in this Review is not just centred about the Frozen Formalism Problem facet, but rather about each of the eight facets. Particular emphasis is placed upon A) relationalism as an underpinning of the facets and as a selector of particular strategies (especially a modification of Barbour relationalism, though also with some consideration of Rovelli relationalism). B) Classifying approaches by the full ordering in which they embrace constrain, quantize, find time/history and find observables, rather than only by partial orderings such as “Dirac‐quantize”. C) Foliation (in)dependence and Spacetime Reconstruction for a wide range of physical theories, strategizing centred about the Problem of Beables, the Patching Approach to the Global Problem of Time, and the role of the question‐types considered in physics. D) The Halliwell‐ and Gambini–Porto–Pullin‐type combined Strategies in the context of semiclassical quantum cosmology.     

圈量子引力中面积与体积算符本征作用的估值

用统一处理几何算符作用的方法及所得的结果,获得了一种完备的面积谱.并对Thiemann的Hamilton约束中的欧氏项的作用给出了不同解释与结果.在图式法处理抓作用中,通过化简,给出了抓任意三重组对任何n顶角作用的重耦矩阵表式.用抓作用的移动法,推算出了抓的任意三重组对任意价顶角作用的重耦矩阵的完整、精确的一般表式. 关键词： 体、面积算符作用的统一表述 完备面积谱 抓作用的化简 重耦矩阵一般表式     

Finite field-dependent symmetries in perturbative quantum gravity

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation.     

Loop quantum gravity modification of the Compton effect

Modified dispersion relations (MDRs) as a manifestation of Lorentz invariance violation, have been appeared in alternative approaches to quantum gravity problem. Loop quantum gravity is one of these approaches which evidently contains modification of dispersion relations. These MDRs will affect the usual formulation of the Compton effect. The purpose of this paper is to incorporate the effects of loop quantum gravity MDRs on the formulation of Compton scattering. Using limitations imposed on MDRs parameters from ultra high energy cosmic rays (UHECR), we estimate the quantum gravity-induced wavelength shift of scattered photons in a typical Compton process. Possible experimental detection of this wavelength shift will provide strong support for underlying quantum gravity proposal.     

An alternative description of gabor spaces and gabor-toeplitz operators

We show a representation of the spaces of Gabor transforms using the general decomposition method of Vasilevski. This provides an interesting characterization of a class of Gabor-Toeplitz operators and enables to obtain their representation formulae, Wick calculus and the commutativity of the algebra of such operators particularly simply.     

利用信息流方法优化多激发自旋链中的量子态传输

研究了量子态在一条均匀耦合的反铁磁自旋链中传输时, 信道中自旋激发数变化对其传输性质的影响. 利用信息流方法分析输出端粒子的算符演化动力学, 获得了量子态传输的平均保真度与信道自旋初态之间的关系. 结果表明, 平均保真度的大小只依赖于信道中自旋激发数的奇偶性. 通过比较在奇偶激发信道中获得的最大平均保真度, 构建了优化信道来提升量子态在自旋链中的传输质量. 进一步分析了纠缠在激发信道中的传输情况, 发现纠缠的传输质量不仅和信道中自旋激发的具体个数有关, 还取决于激发自旋的初始排列. 特别地, 当信道中自旋无激发或全部激发时, 纠缠传输的大小和持续时间都优于其他的激发信道. 上述研究结果有助于在实际系统中搭建适合量子态和纠缠传输的量子信道.     

Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Recently,considerable progress has been made in understanding the early universe by loop quantum cosmology.Modesto et al.investigated the loop quantum black hole(LQBH)using improved semiclassical analysis and they found that the LQBH has two horizons,an event horizon and a Cauchy horizon,just like the Reissner-Nordstr¨om black hole.This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background.By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method,we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly.However,the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value.We also find that the loop quantum gravity area gap parameter a 0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer.In the complex ω plane,the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.     

Exact uncertainty approach in quantum mechanics and quantum gravity

The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of motion to the Schrödinger equation. This ‘exact uncertainty’ approach may be generalised to ensembles of gravitational fields, where nonclassical fluctuations are added to the field momentum densities, of a magnitude determined by the uncertainty in the metric tensor components. In this way one obtains the Wheeler-DeWitt equation of quantum gravity, with the added bonus of a uniquely specified operator ordering. No a priori assumptions are required concerning the existence of wave functions, Hilbert spaces, Planck's constant, linear operators, etc. Thus this approach has greater transparency than the usual canonical approach, particularly in regard to the connections between quantum and classical ensembles. Conceptual foundations and advantages are emphasised.     

Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces

We give formulas for integration by parts over the path space and over the loop space of a manifold. We define Sobolev spaces and an Ornstein-Uhlenbeck operator on the loop space. We find some functionals which belong to all the Sobolev spaces.     

一种空时体积与引力的激发和跃迁生成模式

利用4单形及其对偶1-骨架,描述了纯空时的跃迁. 对自旋网编织成的三维空间在跃迁的两个台阶间体积的改变做出了证明. 给出了四维空时体积的一个平坦量子涨落模型. 利用自旋网腿中的圈线刺过曲面时产生的激发,获得了三维空间的2阶对称离散张量h^ab,按照空时是激发和跃迁体系的观点,得到了离散引力场h^μν的产生与改变机制. 关键词： 体积量子膨胀 空时度规涨落 引力扰动的激发 2阶对称张量的产生