爱因斯坦引力场Arnowitt-Deser-Misner约束方程的两种推导方法

给出两种不同方法,分别导出爱因斯坦引力理论中著名的Arnowitt-Deser-Misner(ADM)约束方程.其一是在具有洛伦兹号差的时空中,构造一个单参数引力场作用量,由此导出单参数ADM约束方程.该参数取某特定值时对应的就是熟知的ADM约束方程.其二是将二重复函数理论运用于爱因斯坦引力场的哈密顿形式表述中,得到引力场ADM约束的二重化形式,从而也能将通常的ADM约束作为其特殊情况包含其中.此外,这两种方法还能统一地表述具有不同时空号差(洛伦兹号差和欧几里得号差)的洛伦兹引力理论和欧几里得引力理论 关键词： Arnowitt-Deser-Misner约束方程 哈密顿表述 时空号差 引力场作用量     

浅谈广义相对论的创立之二 广义相对性原理的确立

简述了广义相对性原理确立的历程、马赫思想的影响、广义相对性原理由一般表述发展到严格表述的过程,介绍了高斯坐标及其在引力场中的应用,说明了度规系数gμν是描述引力场的基本张量.     

遥远星体在太阳引力作用下形成的爱因斯坦环

当遥远星体,太阳以及观测者在一条直线上时,由于星光在太阳引力场中的偏折效应将形成爱因斯坦环.忽略太阳自转,其外部引力场可用史瓦西度规描述.运用椭圆积分严格地求出零测地线的精确解,并从精确解反解出观测者的径向坐标.从零测地线的精确解可计算出观测者与太阳的距离必须大于或等于547.7天文单位才能观测到星光在太阳引力作用下产生的爱因斯坦环,但是爱因斯坦环几乎和太阳边缘重叠在一起,目前的技术难以分辨.     

非对易相空间中的狄拉克振子的能级和Wigner函数

非对易几何、弦论和圈量子引力理论的发展,使非对易空间受到越来越多的关注.非对易量子理论不同于平常的量子理论,它是弦尺度下的特殊的物理效应,处理非对易量子力学问题需要特殊方法.本文首先介绍了Moyal方程与Wigner函数,利用Moyal-Weyl乘法与Bopp变换将H(x,p)变换成^H(^x,^p),考虑坐标—坐标、动量—动量的非对易性,实现对非对易相空间中星乘本征方程的求解.并利用非对易相空间量子力学的代数关系,讨论了非对易相空间中狄拉克振子的Wigner函数和能级,研究结果发现非对易相空间中狄拉克振子的能级明显依赖于非对易参数.     

量子几何与三旋

量子几何避开使用度规场，从而也不再引进所谓的背景度规，因此被称为是一种与背景无关的量子引力理论。但它以联络作为引力理论的基本变量，体现了将引力场视为规范场的物理思想。不仅如此，自旋联络作为引力理论的基本变量也为进一步研究这种耦合提供了舞台。传统的量子几何与超弦理论目前还是两个独立的理论，彼此之间唯一明显的相似之处是两者都使用了一维的几何概念作为理论基础。如果这两个理论都反映了物理世界某些本质特征，那么这种相似性也许就不是偶然的。三旋理论的研究已揭示出这种巧合背后的联系之谜。     

二维模糊球上的量子霍尔流体

在回顾了Haldane对量子Hall效应在二维球面S2上的描述后,本文构造了二维模糊球S2上的非对易代数及其Hilbert空间的Moyal结构.通过构造模糊球上不可压缩量子霍尔流体的非对易Chern-Simons理论,求解具有准粒子源的Gaussian约束,找出模糊球上的Calogero矩阵及最低Landau能级Laughlin波函数的完全集,此Laughlin波函数由旋量坐标推广的Jack多项式表示.     

含曲率二次项的强引力

本文指出,一个de-Sitter型的强引力度规,在引入曲率标量二次项修正后,可保持度规形式不变.但是,由于二次项的作用.等价于使强引力耦合系数G_f相应减小,这说明二次项的修正可以导致一个合理的强引力而避免奇异性.     

旋转物体的等效原理及其空间实验

文章回溯了等效原理的历史,解释了弱等效原理(伽利略等效原理)、强等效原理(爱因斯坦等效原理)和甚强等效原理.实验检验表明,到10-13的实验精度时,没有观测到等效原理的破坏.文章最后,也是文章的主要目的,阐述了广义相对论的不足,即不能描写物质的自旋与引力场的耦合.自旋粒子或自转物体的能一动张量既有对称分量,也有非对称的分量,还有自旋张量.但是广义相对论的引力场方程中只包含了能-动张量对称分量,不包含反对称分量,更没有自旋张量的贡献.涉及自旋与引力场耦合的理论是(有挠率场的)引力规范理论,该理论预言:自旋粒子或旋转物体将偏离测地运动,因而破坏等效原理.为了检验这种破坏,文章作者及其合作者建议进行地面实验和空间实验.     

二维阻尼谐振子在非对易空间中的能级

非对易空间效应是出现在弦的尺度下的一种物理效应.文章介绍了非对易空间中量子力学的代数关系,在所考虑的空间变量的对易关系中包含了坐标-坐标的非对易性,并且把Moyal-Weyl乘法在非对易空间中通过Bopp's变换转变成普通的乘法.然后给出了二维阻尼谐振子在非对易空间的能级分裂情况.     

耗散系统不可逆过程中的可拓展广义相对论时空关系

在引入非保守非惯性系的基础上对不可逆过程建立非保守系等效性假设，在引入广域度规的基础上对具有复杂行为的时空建立非保守系协变性假设；利用密度分布的不均匀度h(ρ)和粗粒熵S（ρtε）及推导的多标度因数η*计算式，引入非保守惯性质量和非保守引力质量.分析表明，新结果使引力理论与非平衡态统计理论和非线性动力学达到应有的谐和，发展并修正广义相对论. 关键词： 时空关系 耗散系统 不可逆性 可拓展广义相对论 非保守引力质量     

Differential and Complex Geometry of Two-Dimensional Noncommutative Tori

We analyze in detail projective modules over two-dimensional noncommutative tori and complex structures on these modules. We concentrate our attention on properties of holomorphic vectors in these modules; the theory of these vectors generalizes the theory of theta-functions. The paper is self-contained; it can be used also as an introduction to the theory of noncommutative spaces with simplest space of this kind thoroughly analyzed as a basic example.     

The Complex Symmetry Gravitational Theory as a New Alternative of Dark Energy

We propose that complex symmetry gravitational theory (CSGT) explain the accelerating expansion of universe. In this paper, universe is taken as the double complex symmetric space. Cosmological solution is obtained within CSGT. The conditions of the accelerating expansion of universe are discussed within CSGT. Moreover, the range of equation of state of matter ω_ε is given in the hyperbolic imaginary space. PACS: 98.80Es, 04.20Fy     

Particles and Scalar Waves in Noncommutative Charged Black Hole Spacetime

In this paper we have discussed geodesics and the motion of test particle in the gravitational field of noncommutative charged black hole spacetime. The motion of massive and massless particle have been discussed seperately. A comparative study of noncommutative charged black hole and usual Reissner—Nordström black hole has been done. The study of effective potential has also been included. Finally, we have examined the scattering of scalar waves in noncommutative charged black hole spacetime.     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.     

Effective Action for Noncommutative U(1) Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U(1) gauge theories. This assumption is that the noncommutative effects start to be visible continuously from a scale λ_NC and that below this scale the theory is a commutative one. Based on thisassumption and using background field method and loop calculations, an effective action is derived for noncommutative U(1) gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. Thecoefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

3D quantum gravity and effective noncommutative quantum field theory

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.     

Star Product Formula of Theta Functions

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.     

On the problem of reality conditions for the Ashtekar formulation

In this paper we discuss the reality conditions for Lorentzian and Euclidean gravity in the Ashtekar formulation by introducing a double conformal transformation.We generalize Marugan‘s results and demonstrate that the values of the double conformal factor have to be either real or double complex numbers.Either Lorentzian or Enclidean gravitational theory is up to the different values of the double conformal factor.Furthermore,the reality conditions of Lorentzian and Euclidean gravitational theory can be expressed in a unified way be use of the double complex function method.     

Bi-Hamiltonian structure of the extended noncommutative Toda hierarchy

The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the bi-Hamiltonian structure and noncommutative conserved densities of the extended noncommutative Toda hierarchy by means of the R-matrix formalism. This extended noncommutative Toda hierarchy can be reduced to the extended multicomponent Toda hierarchy, extended Z_N?-Toda hierarchy, extended Toda hierarchy respectively by reductions on Lie algebras.