Lorentz transformation on the lattice

We study the possibility of representing the kinematical variables of a free particle in terms of scale factors and integers. The action of a set of transformations from the Lorentz group parametrized by integers on this system of variables are investigated, and it is shown that one can effectively characterize these symmetries on a lattice in this way. By taking the scales sufficiently small, one can arbitrarily closely approach the continuous case.Work supported in part by the Binational Science Foundation (BSF) Jerusalem. Israel.     

洛伦兹变换的一种新推导

对于洛伦兹变换中两个惯性系S和S′系的约定提出了新思路,使x轴与x′轴反向,从而使S和S′系完全对称,简化了推导过程;并根据约定,从狭义相对论的两条基本假设出发,严格地推导出了洛伦兹变换式.     

Lorentz transformation of three dimensional gravitational wave tensor

Recently there has been more and more interest in the gravitational wave(GW) of moving sources. This paper introduces a Lorentz transformation problem of GWs. Although the BondiMetzner-Sachs(BMS) theory has in principle already included the Lorentz transformation of GWs, the transformation of the three-dimensional GW tensor has not been explicitly calculated before. Within four-dimensional spacetime, GWs have the properties of ‘boost weight zero’ and‘spin weight 2’. This fact makes the Lorentz t...     

On the possibility of a three-temporal Lorentz transformation

It is suggested that, strictly speaking, light speed invariance would not seem to be fully consistent with ordinary space geometry unless proper time is allowed to undergo one independent dilatation for each degree of space freedom.     

洛伦兹速度变换的一种直接推导方法

用光速不变原理直接导出洛伦兹速度变换式，并证明相对论性速度构成双曲几何的Beltrami-Klein模型。     

再谈洛伦兹变换的推导

评论了仅仅依据光速不变假设和相对性原理推导洛伦兹变换公式的方法.     

Spectral representations of Lorentz invariant distributions and scale transformation

An approach to the theory of Lorentz invariant distributions is developed in terms of covariant spectral representations. The behaviour of singular invariant distributions under a change of scale is analyzed. It is shown that the conventional extension of homogeneous singular functions into distributions inR ⁴, followed by a breakdown of homogeneity, is incomplete. Homogeneous extensions depending on an arbitrary scaling parameter are introduced, calculation techniques are developed and various formulae having applications in quantum field theory are derived.Supported by the Deutsche Forschungsgemeinschaft.     

Dual properties of spacetime under an alternative Lorentz transformation

In flat spacetime, the fourth space coordinate in special relativity (SR) is equivalent to the coordinate time t_E. We will show, however, that this definition of physical time is not unique. Another natural choice of coordinate time, t_A, with absolute synchronization is allowed. Spacetime would exhibit dual properties, namely relativistic and absolute. In an arbitrary inertial frame, the relationship of the above two kinds of coordinate time corresponds to a resynchronization, and the Lorentz transformations can be written in an alternative form, which is called the generalized Galilean transformation (GGT). Although the absolute property is still hidden in nearly all types of experiments, the advantages of the above approach are as follows: (1) It will give us a deeper understanding of SR, including the basis of length contraction, time dilation and the interaction between moving objects and the physical vacuum. (2) It will provide a wider research domain than SR; for example, superluminal motion is predicted and has obtained growing experimental support.     

Lorentz变换和Maxwell方程的最简单形式

用Cifford代数来描述，Lorents变换和Maxwell方程组变得非常简单。例如，Maxwell方程成为□F=4πj/c，只一个方程就够了。     

A note on Lorentz transformation properties of conserved charges

It is shown that in classical relativistic field theories there may exist global conserved charges which are not Lorentz-covariant quantities.     

无需利用洛伦兹变换的相对论质能关系新推导

依据相对性原理以及相对论动量、能量的基本定义和相应的动量守恒、能量守恒定律,针对静质量不为零的粒子,给出一种无需依赖运动学具体时空变换关系而主要在动力学范围内得到相对论质能关系的新推导.     

Geodesic Connectedness in Generalized Reissner-Nordström Type Lorentz Manifolds

A detailed study of the existence, causal character and multiplicity of geodesics joining two points is carried out for a wide family of non-static Lorentz manifolds (including intermediate Reissner-Nordström, inner Schwarzschild and Generalized Robertson-Walker spacetimes). Results relating causality and connectedness by timelike or lightlike geodesics are obtained, in the spirit of the well-known Avez-Seifert result. The existence of closed spacelike geodesics is also characterized.     

Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation axis of a spinning mass, Thomas rotation gives rise to the well-knownThomas precession. A 3×3 parametric, unimodular, orthogonal matrix that represents the Thomas rotation is presented and studied. This matrix representation enables the Lorentz transformation group to be parametrized by two physical observables: the (3-dimensional) relative velocity and orientation between inertial frames. The resulting parametrization of the Lorentz group, in turn, enables the composition of successive Lorentz transformations to be given by parameter composition. This composition is continuously deformed into a corresponding, well-known Galilean transformation composition by letting the speed of light approach infinity. Finally, as an application the Lorentz transformation with given orientation parameter is uniquely expressed in terms of an initial and a final time-like 4-vector.     

Equilibration,Generalized Equipartition,and Diffusion in Dynamical Lorentz Gases

We demonstrate approach to thermal equilibrium in the fully Hamiltonian evolution of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a d-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We analytically predict, and numerically confirm, that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature T, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics—they need not be in a state of thermal equilibrium. The temperature T to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy k _B T is equal to an appropriately defined average of the scatterers’ kinetic energy. In the equilibrated state, particle motion is diffusive.     

Generalized transformation for decorated spin models

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.     

Comment on “on the possibility of a three-temporal Lorentz transformation”

In a recent paper it has been suggested that, strictly speaking, light speed invariance is not fully consistent with ordinary space geometry unless our concept of time is drastically modified. This note argues against that paper.     

时空间隔在所有的惯性系中保持不变与洛伦兹变换

在狭义相对论的框架下,文中首先论述了在时空间隔保持不变的条件下,惯性系之间的时空变换一定是线性的,随后证明了在这一条件下惯性系之间的时空变换必定也是唯一的,最后证明了这唯一的时空变换就是洛伦兹变换.因此从时空间隔保持不变这一条件出发完全可以建立洛伦兹变换,文中在最后一节还论证了这一建立洛伦兹变换的条件是最基本的条件,没有其他更低的条件.     

Generalized symmetry transformation with Gaussian phase weight function

The generalized symmetry transformation (GST) is a symmetry operator detecting objects by using edge gradient directions. Conventional GST uses the cosine function to define the phase weight function (PWF), which represents the symmetry of two gradient directions. The cosine function of PWF leads to a good performance in detecting symmetrical objects. However, the weights of gradient pairs, which are considered to be asymmetrical, are relatively high, so side effects appear near the symmetry pick regions. (Note that side effects disturb the multiple object detection.) In this paper, we use the Gaussian function in calculating the symmetric weights of gradient pairs. The Gaussian function can suppress the weights of less symmetric gradient pairs. In addition, the symmetry for elliptically shaped objects can be more emphasized by controlling the width of the Gaussian function. The proposed GST is evaluated through experiments on synthetic images, which include various bright and dark plane figures, and on real images, which requires the detection of elliptical shapes.     

经典洛伦兹磁力和广义洛伦兹磁力解释电子感应加速器的本质

介绍了虚构的法拉第定律与电子感应加速器不合理,用完整洛伦兹磁力解释电子感应加速器合理有效。