宇宙常数问题

在共形引力理论中, 宇宙项必为零. 当所有规范对称性自发破缺时, 产生的诱导宇宙常数之和与背景时空的弯曲效应抵消. 当背景时空为Minkowski空间时, 诱导宇宙常数之和为零. 而对称性通过Higgs机制破缺时, 必然伴生背景时空的相变.     

R-W宇宙中的Dirac真空解

本文将文献[5]的结论推广到R-W宇宙中的旋量场,求得无质量时的严格解Ω_n=n/a,它对应一个共形真空.在有质量的情况下,_n=m+n/a,它对应一个绝热真空.     

Lagrange系统的共形不变性与Hojman守恒量

研究了一般完整Lagrange系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,并且找到在特殊无限小变换下的共形不变性并且是Lie对称性的共形因子,接下来导出Lagrange系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例. 关键词： Lagrange系统 共形不变性 Hojman守恒量 确定方程     

广义Hamilton系统的共形不变性与Hojman守恒量

研究了广义Hamilton系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,找到在无限小变换下的共形不变性并且是Lie对称性的共形因子,最后导出广义Hamilton系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例. 关键词： 广义Hamilton系统 共形不变性 Hojman守恒量 确定方程     

全局稳定性一致的共形卷积完全匹配层

在正交网格体系中建立物理模型共形描述的基础上,针对采用扩展元胞技术的共形时域有限差分(ECT-CFDTD)方法模拟计算波导器件遇到的开放端口截断问题,给出了积分形式的共形卷积完全匹配层方法,算法具有与ECT-CFDTD相同的数值稳定性。设置不同的完全匹配层的控制参数,对波导中有消逝波存在的情况进行长时间模拟计算,分析共形卷积完全匹配层对消逝波的长效截断能力,分析卷积完全匹配层的截断误差。计算结果显示:积分形式的共形卷积完全匹配层可有效截断波导器件的开放端口。     

基于倾斜光学元件的共形光学窗口瞄视误差校正

为校正共形光学窗口引入的随扫描视角变化而变化的动态瞄视误差,提出基于倾斜光学元件的瞄视误差校正。建立共形光学窗口的瞄视误差模型,并分析计算共形光学窗口引入的动态瞄视误差。阐明利用倾斜光学元件校正共形光学窗口瞄视误差的原理,并通过在共形光学窗口后加入倾斜的球面透镜予以证明。给出一个设计实例,通过将校正共形光学窗口像差的校正元件倾斜,实现共形光学窗口的瞄视误差校正,且并未影响共形光学窗口像差的校正。     

变质量完整系统的共形不变性和Noether对称性及Lie对称性

研究变质量完整系统在无限小变换下的共形不变性与Noether对称性和Lie对称性.首先,给出了变质量完整系统的共形不变性的定义;其次,研究了系统的共形不变性与Noether对称性之间的关系,得到了共形不变性导致的Noether守恒量;最后,研究了系统的共形不变性与Lie对称性之间的关系,得到了共形不变性同时是Lie对称性导致的Hojman守恒量.最后举例说明了结果的应用.     

基于反向旋转位相板的共形光学系统设计

在共形光学系统中,椭球形整流罩打破了球形整流罩的旋转对称性,引入了随目标视场变化而变化的动态像差。共形光学设计的主要任务就是消除或者减小椭球形整流罩引入的动态像差,使共形光学系统的成像质量满足使用要求。设计了基于反向旋转位相板的共形光学系统,利用一对反向旋转位相板的反向旋转对目标视场进行动态扫描,利用固定校正器、衍射元件和泽尼克位相板校正了椭球形整流罩引入的动态像差。成像系统采用二次成像的透射式结构,实现了冷光阑效率100%。结果表明:该方法不仅有别于传统扫描方式,而且有效地消除了大长径比的共形光学系统的动态像差。     

变质量完整动力学系统的共形不变性与守恒量

研究变质量完整力学系统在无限小变换下微分方程的共形不变性.提出了该系统共形不变性的概念,推导出变质量完整力学系统运动微分方程具有共形不变性,同时又是Lie对称性的充分必要条件.得到由共形不变性导致的Noether守恒量. 关键词： 变质量系统 无限小变换 共形不变 守恒量     

消像差条件在共形光学系统中的应用

根据轴对称光学系统中的消像散条件探讨了共形整流罩结构中消像散万向节点位置的存在性.在此基础上,对共形光学系统中消像差万向节点位置进行了理论推导.软件分析结果表明,轴对称光学系统消像差条件对于共形光学系统的设计仍有良好的指导意义,由此得到的"消像差"共形光学系统的残余像差已处于实际成像系统的像差校正能力范围之内.     

Hidden conformal symmetry and pair production near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter spacetime

We show that the study of the hidden conformal symmetry that is associated with the Kerr/CFT correspondence can also apply to the cosmological horizon in the Kerr-Newman-Taub-NUT-de Sitter spacetime. This symmetry allows employing some two dimensional conformal field theory methods to understand the properties of the cosmological horizon. The entropy can be understood by using the Cardy formula, and the equation for the scattering process in the near region is in agreement with that obtained from a two point function in the two-dimensional conformal field theory. We also show that pair production can occur near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter for near extremal conditions.     

Conformal Anomaly and Large-ScaleGravitational Coupling

We present a model in which the breakdown of conformal symmetry of a quantumstress-tensor due to the trace anomaly is related to a cosmological effect in agravitational model. This is done by characterizing the traceless part of thequantum stress-tensor in terms of the stress-tensor of a conformal invariantclassical scalar field. We introduce a conformal frame in which the anomaloustrace is identified with a cosmological constant. In this conformal frame weestablish the Einstein field equations by connecting the quantum stress-tensorwith the large-scale distribution of matter in the universe.     

A kinematical approach to conformal cosmology

We present an alternative cosmology based on conformal gravity, as originally introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas. Unlike past similar attempts our approach is a purely kinematical application of the conformal symmetry to the Universe, through a critical reanalysis of fundamental astrophysical observations, such as the cosmological redshift and others. As a result of this novel approach we obtain a closed-form expression for the cosmic scale factor R(t) and a revised interpretation of the space–time coordinates usually employed in cosmology. New fundamental cosmological parameters are introduced and evaluated. This emerging new cosmology does not seem to possess any of the controversial features of the current standard model, such as the presence of dark matter, dark energy or of a cosmological constant, the existence of the horizon problem or of an inflationary phase. Comparing our results with current conformal cosmologies in the literature, we note that our kinematic cosmology is equivalent to conformal gravity with a cosmological constant at late (or early) cosmological times. The cosmic scale factor and the evolution of the Universe are described in terms of several dimensionless quantitites, among which a new cosmological variable δ emerges as a natural cosmic time. The mathematical connections between all these quantities are described in details and a relationship is established with the original kinematic cosmology by L. Infeld and A. Schild. The mathematical foundations of our kinematical conformal cosmology will need to be checked against current astrophysical experimental data, before this new model can become a viable alternative to the standard theory.     

Conformal aspects of the Palatini approach in Extended Theories of Gravity

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of Palatini approach which allows to distinguish between spacetime structure and geodesic structure. These facts are relevant at least at cosmological scales, while at small scale (i.e. in the spacetime regions relevant for observations) the conformal factor is slowly varying and its effects are not relevant. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frame are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

Non-singular space-times with a negative cosmological constant: II. Static solutions of the Einstein–Maxwell equations

We construct infinite-dimensional families of non-singular static space-times, solutions of the vacuum Einstein–Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.     

Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.     

Conformal Invariance, Accelerating Universe and the Cosmological Constant Problem

We investigate a conformal invariant gravitational model which is taken to hold at early universe. The conformal invariance allows us to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transition, the resulting mass scale introduced by particle physics should have a variable contribution to vacuum energy density. This variation is controlled by the conformal factor which is taken as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.     

The cosmological constant and conformal invariance

A scheme is given in N = 1 Poincaré + conformal supergravity in such a way that the induced cosmological constant is necessarily vanishing when the conformal invariance is spontaneously broken.