Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity(TEGR).A spacetime which is not asymptotically flat is derived.The energy conditions of this spacetime are studied.It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy.The singularities of this solution are discussed.     

A canonical dynamics view of the Newtonian limit of general relativity

The Newtonian limit of general relativity was Jürgen Ehlers favourite model for limit relations between theories of physics. In this contribution, for the case of isolated systems, the Newtonian limit of general relativity will be illuminated from a canonical dynamics point of view. The canonical dynamics approach naturally supplies a post-Newtonian expansion of general relativity.     

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443–461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43–103, 1990) for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.      

动能定理应用中的一个问题

针对某些不能实现（一般在计算前不知能否实现）的题设运动，动能定理积分形式也有“解”的情况，用两个例子分析了问题的原因，指出了动能定理积分形式应用中的注意点和验证解是否与实验吻合的途径。     

Canonical quantization theory of general singular QED system of Fermi field interaction with generally decomposed gauge potential

Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system.     

The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

关于力学相对性原理和机械能守恒定律的讨论也谈机械能守恒定律和相对性原理

指出机械能守恒定律是服从相对性原理的.     

A comparative analysis of the adiabatic stability of anisotropic spherically symmetric solutions in general relativity

A family of static solutions of the Einstein field equations with spherical symmetry for a locally anisotropic fluid with homogeneous energy density is obtained. These solutions depend on two adjustable parameters related to degree of anisotropy of the fluid. Some known solutions may be recovered for specific values of these parameters. As a difference to other known solutions it is possible to change the grade of anisotropy of the model, keeping the same functional dependence on the coordinates. By means of a slow adiabatic contraction, the stability of the obtained solutions is studied. Also, it is shown, how it is possible to enhance the stability of the models by adjusting the parameters, and to obtain more compact configurations than those obtained with other similar anisotropic solutions, while the dominant or strong energy condition holds within the sphere.     

爱丁顿与广义相对论的验证

简单介绍了在广义相对论诞生之初,验证其理论正确性的三个天文实验,并详细介绍了爱丁顿为验证广义相对论,发起并组织的观测1919年5月29日的日全食考察队的具体情况.这是爱丁顿认为他在天文学研究中最激动人心的事件.     

The physical role of gravitational and gauge degrees of freedom in general relativity – II: Dirac versus Bergmann observables and the objectivity of space-time

This is the second of a couple of papers in which we aim to show the peculiar capability of the Hamiltonian ADM formulation of metric gravity to grasp a series of conceptual and technical problems that appear to have not been directly discussed so far. In this paper we also propose new viewpoints about issues that, being deeply rooted into the foundational level of Einstein theory, seem particularly worth of clarification in connection with the alternative programs of string theory and loop quantum gravity. The achievements of the present work include: (1) the analysis of the so-called Hole phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of spatially non-compact Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the weak ADM energy. It is crucial to our analysis the re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (nearly unknown) connection to gauge transformations on-shell; this is expounded in the first paper (gr-qc/0403081); (2) the utilization of the Bergmann-Komar intrinsic pseudo-coordinates, defined as suitable functionals of the Weyl curvature scalars, as tools for a specific gauge-fixing to the super-hamiltonian and super-momentum constraints; (3) the consequent construction of a physical atlas of 4-coordinate systems for the 4-dimensional mathematical manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent Dirac observables). Such construction embodies the physical individuation of the points of space-time as point-events, both in absence and presence of matter, and associates a non-commutative structure to each gauge fixing or 4-dimensional coordinate system; (4) a clarification of the multiple definition given by Peter Bergmann of the concept of (Bergmann) observable in general relativity. This clarification leads to the proposal of a main conjecture asserting the existence of: i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) change in the observable quantities of general relativity; (5) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a standard of space-time more or less like atomic clocks define standards of time. In the end, against the well-known Einstein's assertion according to which general covariance takes away from space and time the last remnant of physical objectivity, we conclude that point-events maintain a peculiar sort of objectivity. Also, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of participating directly in the individuation process, being involved in the determination of the Dirac observables. Finally, some hints following from our approach for the quantum gravity programme are suggested.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

澄清对相对论性原理和协变性的误解

近来有些文章断言,在一个惯性参考系里能量守恒的物理系统,在别的参考系看来能量也一定守恒.实际上这些作者混淆了物理方程式的协变性和相对性原理.本文将澄清这一误解.     

机械能守恒定律服从力学相对性原理

阐述了机械能守恒定律服从力学相对性原理。     

On the AKSZ Formulation of the Poisson Sigma Model

We review and extend the Alexandrov–Kontsevich–Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin–Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.     

耗散系统不可逆过程中的可拓展广义相对论引力关系

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，将Weyl曲率拓展为多标度曲率R*；利用与物理量在几何上的奇异性分布有关的多重分形，初步建立嵌入Riemann空间的生长结构多重分形几何；在此基础上，通过引入与分形维数、信息维数和关联维数有关的广义维数Du，建立非保守引力场方程.分析表明：新结果为解决宇宙学奇性、星系团的“不明物质”、黑洞的信息疑难、引力理论与量子物理的统一等问题提供适当基础. 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     

On the accuracy of wavefunctions obtained by the Fourier grid Hamiltonian method

The quality of wavefunctions obtained by the Fourier grid Hamiltonian (FGH) method is analyzed. The criteria used for judging the quality are the extent to which virial, hypervirial and Hellmann-Feynman theorems are satisfied by the numerically computed FGH-wavefunction. The quality of the FGH-wavefunction is also examined from the point of view of local error in the wavefunction. It is shown that high quality wavefunctions can be obtained from the FGH recipe if the grid length (L) and grid spacings are chosen after properly examining the range of the potential and its nature.