相对论性力学系统的Birkhoff对称性与守恒量

提出了相对论性力学系统的一种新的对称性,并给出了此对称性导致的守恒量.提出了相对论性力学系统的Birkhoff对称性,即对应于相对论性力学系统的一组Birkhoff动力学函数的运动微分方程的解都满足从另一组Birkhoff动力学函数得到的运动微分方程.证明了与两组Birkhoff动力学函数分别给出的相对论性Birkhoff方程相关联的系数矩阵的各次幂的迹是系统的一个守恒量,从而将Currie和Saletan提出的力学系统的等效Lagrange函数定理拓展到了相对论性Birkhoff动力学系统.给出了两个例子以说明结果的正确性.     

等离子体中相对论性电子回旋波色散关系

推导了一般条件下的相对论性电子回旋波色散关系。其中采用了相对论性修正的分布函数。对奇点作了较好的处理。所得到的公式可直接用于计算一般条件下的相对论性电子回旋波的传播和吸收问题。为高温等离子体波的研究提供了一个很方便的理论公式。 关键词：     

极端相对论性正负电子对等离子体中横振荡的色散关系

 由伏拉索夫方程和费米分布函数的相对论性修正形式推导出相对论性正负电子对等离子体中横波的色散方程,对等离子体中的横波进行解析研究,得到长波支和短波支的色散关系。从解析的色散曲线发现了与Mikhailovskii在极端相对论性情况下对于电子-离子等离子体中色散关系研究相类似的结果:在极端相对论性等离子体中横波的解析色散曲线具有不连续性。基于解析色散曲线的不连续性,进而采用数值计算的方法求解了完整的等离子体色散方程,得到其数值解,数值色散曲线可将解析上的长波和短波衔接起来,使其成为一条完整的色散曲线。     

相对论性变质量系统的守恒律

研究相对论性变质量系统的守恒律.给出相对论性变质量系统的d’Alembert-Lagrange原理,利用其在无限小变换下的不变性条件,得到相对论性变质量系统的守恒律存在的条件和形式,并举例说明结果的应用 关键词： 相对论 分析力学 变质量 守恒律     

电子束与等离子体相互作用中的反常效应

本文对强流相对论性电子束与靶等离子体相互作用的反常吸收效应进行了理论研究。从符拉索夫方程出发,导出了强流相对论性电子束双流不稳定性效应解,并进行了弱碰撞修正,得到了相应的等离子体波增长率,对不同情况下出现反常效应的条件及机制进行了研究和讨论。     

Beltrami-de Sitter时空中标量和旋量粒子的量子理论

参照在Minkowski时空中,从粒子的相对论性经典理论过渡到量子理论,建立标量粒子和旋量粒子的相对论性波动方程的方案,在Beltrami-de Sitter时空中建立了de Sitter不变的标量粒子和旋量粒子的相对论性量子力学的基本方程,它们恰恰分别是Beltrami-de Sitter时空中的Klein-Gordon方程和Dirac方程。在Beltrami-anti de Sitter时空的同时类空超曲面簇上求解了这些方程,得到了分立的本征值和相应的本征函数。 关键词：     

Dirac方程的数值解法及其在原子总能量计算中的应用

中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.     

相对论性转动变质量系统的Lie对称性与守恒量

给出相对论性转动变质量系统的d’Alembert原理和运动微分方程.利用运动微分方程在无限小变换下的不变性,建立相对论性转动变质量系统的Lie对称确定方程,得到结构方程和守恒量.并举例说明结果的应用 关键词： 相对论 转动 变质量 Lie对称     

相对论性带电粒子束在轴对称电场和磁场中的温度和能量展宽

从单粒子的相对论性运动方程出发,首先解出运动常数,然后用这些运动常数构成符合Vlasov方程的束粒子分布函数,再由该分布函数算出轴对称电场和磁场中相对论性带电粒子束的束温度和能量展宽,并且对弱相对论性情况和强相对论性情况作了讨论。 关键词：     

相对论性Birkhoff系统的对称性摄动及其逆问题

研究在小干扰力作用下相对论性Birkhoff系统的对称性摄动问题.建立了相对论性Birkhoff系统的基本原理、运动方程和小扰动方程.讨论该系统的Lie对称性变换和守恒量.研究在无限小变换下该系统的对称性摄动，构造了s阶绝热不变量.给出了绝热不变量存在的条件和形式.研究该系统的对称性摄动逆问题，当系统存在s阶绝热不变量时，得到了该系统的无限小变换的对称性摄动.研究相对论性Birkhoff系统和经典Birkhoff系统对称性摄动之间的关系. 关键词： Lie对称性 摄动 绝热不变量 相对论     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Statistical mechanics of relativistic plasmas

Based on the Klimontovich method of construction of a relativistic statistical mechanics the binary correlation function of a relativistic plasma is considered. Up to the order e⁴ for spatially homogeneous systems the relativistic binary correlation function can be expressed by the relativistic dielectric tensor, where higher-order correlation functions are neglected.In the case of thermodynamic equilibrium the relativistic dielectric tensor is calculated. The corresponding binary correlation function is determined up to the first relativistic order. The result is compared with those of Trubnikov/Kosachev (1968) and Krizan (1969).     

Basic Aspect of Relativistic Rotation: Franklin Rotation of a Sphere

We give a relativistic treatment to the dynamics of spherical bodies rotating at very high speed. It is found that most of the mass of a homogeneous spherical quark with Franklin rotation is due to the relativistic increase of the mass.     

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Ultrarelativistic excitation of beat waves in a hot magnetized plasma

Summary A theoretical investigation is made on the nonlinear relativistic excitation of an electrostatic electron plasma wave at the beat frequency of two high-power colinear laser beams in a hot, homogeneous and magnetized plasma. The relativistic Vlasov equation expressed in gyrokinetic variables has been employed to find the nonlinear response of the magnetized plasma electrons. It is noted that the power density associated with the excited beat wave is much higher for the relativistic consideration than that for the nonrelativistic consideration. The authors of this paper have agreed to not receive the proofs for correction.     

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导出了无磁化无碰撞各向同性相对论正负电子对等离子体纵波的色散关系。使用逐次近似的标准技术,对两种极限情况下的纵波色散方程进行了解析研究。将完全色散方程进行变换,使它们完全适用于在需要完全相对论处理的温度范围内进行数值计算。用数值模拟方法得到了用解析方法不能得到的完全的色散曲线。     

Quasiclassical distribution function of electrons in a homogeneous magnetic field

Vlasov's equation is used to find the classical nonrelativistic and relativistic distribution functions that describe an electron beam of bounded radius in a homogeneous magnetic field. In the quasiclassical approximation, by means of the exact wave functions of an electron in a homogeneous magnetic field, the quantum relativistic distribution function with allowance for the electron spin is found. The mean physical quantities that characterize the radially bounded electron beam are found as functions of the temperature and electron spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 50–56, July, 1976.It is a pleasant duty to thank Professor V. G. Bagrov for discussing the results.     

稀薄等离子体中的超短强激光脉冲孤子及尾波孤子

在弱相对论条件下，给出了超短强激光脉冲在稀薄等离体中传播的孤子解及其所激发的尾波场孤子解。     

Relativistic Linear Theory in the Absence of External Fields

The dielectric tensor for a multi-component, homogeneous, field-free relativistic plasma is derived in manifestly covariant form. From the dielectric tensor, linear dispersion relations are obtained explicitly when each component of the plasma is isotropic in its rest frame. If the components are relativistic Maxwellians, these dispersion relations are expressible in terms of the relativistic plasma dispersion function. Special attention is given to the Weible and two-stream instabilities and to the normal modes of a quiescent, hot electron gas. For the last case the dispersion relations are solved numerically and compared against computer simulation data. An appendix applies the formalism to cold plasmas.     

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which the obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. We formulate both a special relativistic and a general relativistic versions of Feynman's derivation. Especially in the general relativistic version we prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. We also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context.