Erratum:Classical interpretations of relativistic precessions

We point out an error in Eq.(19) in our original paper [Chin. Phys. B 23 040402(2014)] and present the correct equation.     

Notes on relativistic equations of spin motion

Grounds and applications of Bargmann-Michel-Telegdi equations for the precession of the polarization vector of relativistic particles are considered. A critical question in the discussion is the orientation of the rest frame reference vectors. Møller reference frames which keep constant the mutual orientation of the two infinitely close in time rest frames are shown to have a special role. The generally covariant form of the equations is discussed. The assertion that the principle of relativity is violated in the phenomenon of spin precession is proved to be untrue.     

Noncommutative Geometry and Classical Orbits of Particles in a Central Force Potential

We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential The relation is implemented through the modified commutation relations [xi,xj] = iθij. Comparison with observations places severe constraints on the value of the noncommutativity parameter.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Einstein,de Sitter and the beginning of relativistic cosmology in 1917

In 1917, both Einstein and de Sitter proposed a new interpretation of the universe as a whole: the structure of the universe could be described in terms of relativistic field equations. Their contributions marked the beginning of the modern scientific comprehension of the origin and evolution of the universe. Our aim is to propose a critical review paper, based on references in primary sources, on the formulation in 1917 of Einstein’s and de Sitter’s models of the universe, which represents a fundamental chapter in the history of relativistic Cosmology.     

On the relation of Thomas rotation and angular velocity of reference frames

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in Rindler and Perlick (Gen Rel Grav 22:1067, 1990), is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper (Herrera and di Prisco in Found Phys Lett 15:373, 2002), however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of Rindler and Perlick (Gen Rel Grav 22:1067, 1990) is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of Rindler and Perlick (Gen Rel Grav 22:1067, 1990). Along the way we also establish some general properties of rotating reference frames, which may be of independent interest.     

托马斯效应的简单诠释

托马斯进动的发现对电子自旋概念的确立有重要意义.然而,其物理图像及结论多是采用洛伦兹变换进行连续微分推导而出,过程较为繁杂,掌握难度也较大,在原子物理学教学过程中很难描述.本文通过狭义相对论中长度在运动方向缩短的概念,从电子绕行原子实一周时,在原子实坐标系和电子随动坐标系中最终角度差的积分效应出发,非常简单的论证了1/...     

Decay of de Sitter Vacua by Thermal Activation

Decay of a de Sitter vacuum may proceed through a static instanton, representing pair creation of critical bubbles separated by a distance comparable to the Hubble radius—a process somewhat analogous to thermal activation in flat space. We compare this with related processes recently discussed in the literature.     

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.     

Letter: Weitzenböck Spacetime Outside a Rapidly Rotating Object and the Motion of a Dirac Particle

The tetrad and the torsion fields due to a rapidly rotating massive object are found. The motion of a spin particle in the Weitzenböck spacetime is studied. It is shown that the axial-vector torsion is the entity responsible for the gravitomagnetic component of the gravitational field.The influences of the quadrupole moment of the rapidly rotating object on the motion of the particle are discussed. It is pointed out that the influences of the quadrupole moment are negligible for Kerr black holes, but are as important as that of the Newtonian potential for a rapidly rotating neutron star.     

High energy physics signatures from inflation and conformal symmetry of de Sitter

During inflation, the geometry of spacetime is described by a (quasi‐)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group which acts like a conformal group on : when the fluctuations are on super‐Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three‐dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides the Boltzmann suppression expected from the thermal properties of de Sitter space, the generic effect of heavy fields in the inflationary correlators of the light fields is to introduce power‐law suppressed corrections of the form . This can be seen, for instance, at the level of the four‐point correlator for which we provide the correction due to a massive scalar field exchange.     

Axiomatic approach to the nonassociative group of relativistic velocities

The bizarre and counterintuitive noncommutativity and nonassociativity of the relativistic composition of noncollinear velocities is attributed to the presence of the Thomas rotation. The Thomas rotation, in turn, gives rise to anonassociative group structure for the set of relativistically admissible velocities. This nonstandard group structure has been observed in other contexts and, hence, merits axiomatization.     

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity. In the model, in addition to the cosmological constant, the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy. The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.     

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity

It is shown that all vacuum solutions of Einstein field equation with a positive cosmological constant are the solutions of a model of dS gauge theory of gravity. Therefore, the model is expected to pass the observational tests on the scale of solar systems and explain the indirect evidence of gravitational wave from the binary pulsars PSR1913+16.      

Semi-Classical Derivation of the Spin-Orbit Coupling for the Dirac Particle in an Accelerated Frame

We give a semi-classical derivation for the spin-orbit coupling in the non-relativistic Hamiltonian of the Dirac particle in an accelerated frame, in direct analogy with that for the Thomas term in the case of the electromagnetic interaction.     

经典轨道的封闭性和径向Schr?dinger方程的因式分解

研究表明,保证经典轨道具有封闭性的Bertrand定理可以进一步推广,在适当的角动量下,仍存在着非椭圆的闭合轨道．对于屏蔽Coulomb场,可获得广义Runge-Lenz矢量．这种轨道封闭性与径向Schr?dinger方程因式分解相对应．     

Dirac quasinormal modes of <Emphasis Type="Italic">D</Emphasis>-dimensional de Sitter spacetime

We find exact solutions to the Dirac equation in D-dimensional de Sitter spacetime. Using these solutions we analytically calculate the de Sitter quasinormal (QN) frequencies of the Dirac field. For the massive Dirac field this computation is similar to that previously published for massive fields of half-integer spin moving in four dimensions. However to calculate the QN frequencies of the massless Dirac field we must use distinct methods in odd and even dimensions, therefore the computation is different from that already known for other massless fields of integer spin.     

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity.In the model,in addition to the cosmological constant,the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy.The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.     

Cosmological Evolution of a Ghost Scalar Field

We consider a scalar field with a negative kinetic term minimally coupled to gravity. We obtain an exact non-static spherically symmetric solution which describes a wormhole in a cosmological setting. The wormhole is shown to connect two homogeneous spatially flat universes expanding with acceleration. Depending on the wormhole's mass parameter m the acceleration can be constant (the de Sitter case) or infinitely growing.     

Classical mechanics of directly interacting relativistic particles

We discuss the classical mechanics of relativistic systems containing any number of particles with direct interaction. We continue our previous approach of restricting the observables to gauge invariant variables. As a preliminary we show how to constructN-particle mass shell constraints. Physical momentum and position variables are constructed in consonance with nonsuperluminality and relativity and consistent with a slightly weakened separability which allows the position four vector of separated particles to differ from the canonical coordinate four vector by a constant term which depends on its history but does not affect future dynamics. The formalism is mathematically consistent though slightly more complicated than previous attempts in this direction.