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四维矢量     
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  four-dimensional vector
     use the reletionship of the four-dimensional vector change between the energy and momentum the leads to the changing principle of the applied force between the electric charges, Comment on the reactions between the electric charges in the parellel movement and the reations between the electric charges in the vertical movement.
     利用能量──动量四维矢量变换关系导出电荷间作用力的变换规律,讨论了平行运动电荷间相互作用和垂直运动电荷间的相互作用。
短句来源
  four-dimension vector
     Therefore, A, is confirmed to be a four-dimension vector, which provides a massive foundation of the covariance of these equations under Lorentz transformation.
     特别是对四维势A_μ的变换性质进行了分析,从而确定A_μ是一个四维矢量,使该方程在变换中的不变性有了坚实的基础。
短句来源
  four dimensions vector
     From the angel of four dimensions vector and physics observation, this paper discusses the coordinate transform relationship between the relative movement inertia reference frames.
     文章从四维矢量、物理观测的角度出发,就相互运动惯性系之间的坐标变换关系进行讨论。
短句来源
  4-vector
     By defining four dimensional 'deformation event', the spring's equation about deformation and elasticity becomes perfect covariant 4-vector one.
     在严格定义四维"形变事件"后,弹簧的形变—弹力方程被表达成完全协变的四维矢量方程。
短句来源
     The relativistic relation of radiant heat was educed by transforming energy-momentum 4-vector of a single photon. The elicited results make sure P-E theory of relativistic thermodynamics once again.
     通过单个光子的能量-动量四维矢量变换,导出了辐射热量的相对论关系,所得的结果再一次证实了相对论热力学的P_E理论.
短句来源

 

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      four-dimensional vector
    A formulation of the four-dimensional vector laws of physics which emphasizes the transformation of position and time using the four-vectors (R', 0) and (0,ct') is presented.
          
    It is shown that the geometrical origin of gauge transformations may be found if one considers the eight-dimensional spinor space rather than the four-dimensional vector space as the basis of a physical theory.
          
    It is shown that the geometrical origin of gauge transformations may be found if one considers the eight-dimensional spinor space rather than the four-dimensional vector space as the basis of a physical theory.
          
    Homogeneity for Surfaces in Four-Dimensional Vector Space Geometry
          
    We construct a complete Riemannian metric on the four-dimensional vector space ?4 which carries a two-dimensional space of twistor spinor with common zero point.
          
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      4-vector
    An expression for the current density 4-vector is obtained for the medium under consideration.
          
    An expression for the current density 4-vector is obtained for the medium under consideration.
          
    An expression for the current density 4-vector is obtained for the media considered.
          
    It is shown that, near the mass surface of the real particle, these quantities constitute a 4-vector.
          
    A common assumption in quantum field theory is that the energy-momentum 4-vector of any quantum state must be time-like.
          
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    In this paper, a covariant partial wave analysis of interactions of two particles with low spin value is discussod. Covariant angular momentum operators and relativistic invariant angular quantum numbers are introduced. Using the commutation relations of the covaxiant orbital angular momentum operators and the fou-rdimensional relative momentum operators, the representatives of the covariant orbital angular momenta in the four-dimersional relative momentum representation are uniquely determined, and their eigenfunctions...

    In this paper, a covariant partial wave analysis of interactions of two particles with low spin value is discussod. Covariant angular momentum operators and relativistic invariant angular quantum numbers are introduced. Using the commutation relations of the covaxiant orbital angular momentum operators and the fou-rdimensional relative momentum operators, the representatives of the covariant orbital angular momenta in the four-dimersional relative momentum representation are uniquely determined, and their eigenfunctions are obtained. In the case of particlcles with 1/2 spin and photons, rising the Dirac's equations and the Maxwell's equations, spin operators are defined as the constitutions of the covariant total angular momentum operators. Covariant partial wave analyses for scattering of two particles with O, 1/2 spin, and photoproduction of pious on nucleons are obtained, invariant amplitudes are expressed in terms of relativistic invariant quantities. Usual angular quantum numbers and cosines of scattering angles in the center-of-mass system are replaced by the relativistic invariant angular quantun numbers and scalar products of initial and final four-dimensional relative momenta, respectively. Modulus of total four-momentun take roles as energies in the center-of-mass system in the old noncovariant partial wave analysis. Our results can remove the difficulty that the formalism of angular momontum is not suitable when seeka relativistic invariance in the study of a scattering process through the partial wave expansion.

    本文討論低自旋情况下的两粒子相互作用的协变的分波分析問題。引入了协变的角动量算符和相对論不变的角量子数,利用协变的軌道角动量算符与四維相对动量算符的对易关系,唯一地定出了协变的軌道角动量算符在四維相对动量表象中的表示式和它的本征函数。在自旋1/2的粒子和光子的情况下,利用狄拉克方程和麦克斯威方程,定义了作为协变的总角动量組成部分的自旋算符,并求出了它們与协变的軌道角动量算符的耦合。对自旋0,1/2的粒子的散射和光致产生过程,作出了协变的分波分析,用四維不变量表出了不变振幅。通常的角量子数和质心系中散射角的余弦,現今換成了相对論不变的角量子数和始、末态中的四維相对动量(单位四維矢量)的标量积。非协变分波分析中质心系中的能量的作用,由四維总动量的模来代替。我們的結果消除了在利用分波分析研究散射过程时的角动量公式体系不便保持相对論不变形式的困难。

    For the mathematical description of the basic laws of the classical electromagnetics there existed some different systems and each of them has its own shortcomings. In this paper a new system is presented, which ε_0 and μ_0 in vacuum condition are the pure number 1; that c comes out more naturally than in Gauss system; that "rationalization" comes only from symmetry of space which is more naturally than in MKSA system; that t is alway.acoompanied by c, which will be found better than Gauss system in meeting...

    For the mathematical description of the basic laws of the classical electromagnetics there existed some different systems and each of them has its own shortcomings. In this paper a new system is presented, which ε_0 and μ_0 in vacuum condition are the pure number 1; that c comes out more naturally than in Gauss system; that "rationalization" comes only from symmetry of space which is more naturally than in MKSA system; that t is alway.acoompanied by c, which will be found better than Gauss system in meeting the demands of modern physics during the transition to the four dimensional vector and tensor representation and that the corresponding symmetric relation between the quantities in electricity and in magnetism ran throngh more thoronghly han in Gauss system.

    经典电磁学的规律的数学表述,有许多种不同的结构方案,它们各有其缺点。本文倡议一种新的体系,其中真空的ε_o和μ_o是纯数1;c的出现比高斯制体系来得自然;所谓“有理化”仅仅是考虑了空间的对称性,因而比MKSA制体系来得自然;t总是伴随c出现,所以在过渡到四维矢量及四维张量表示时,比高斯制体系更适用于近代物理的要求;相应的电学量和磁学量间的对称关系比高斯制体系贯穿得更彻底。

    Similar to the magnetic field produced by a moving charge, the gravinetic field can be produced by a moving mass. For instance, a moving straight line mass velocity U parallel to itself and linear density λ, the gravinetic field can be obtained by means of transforma- tion of 4-vector, and the magnitude is b=-(G/c~2) (2ΓλU/r), where Γ=1/((1-(U/c)~2)~(1/2)) .But this article is to avoid the transformation of 4-vector and this article points out that the conception of gravinetic field and gravitational Poynting...

    Similar to the magnetic field produced by a moving charge, the gravinetic field can be produced by a moving mass. For instance, a moving straight line mass velocity U parallel to itself and linear density λ, the gravinetic field can be obtained by means of transforma- tion of 4-vector, and the magnitude is b=-(G/c~2) (2ΓλU/r), where Γ=1/((1-(U/c)~2)~(1/2)) .But this article is to avoid the transformation of 4-vector and this article points out that the conception of gravinetic field and gravitational Poynting vector can be deduced by con- trasting the gravitational field with electrostatic and magnetic. Thus we also obtained the same result. Besides, we add an example which demonstrates the law of conservation of energy in the gravinetic field.

    与运动电荷产生磁场类似,运动质量也能产生类磁引力场。对于线质量密度为λ长直线质量沿其长度方向以速度U运动时,利用四维矢量变换可得到它产生的类磁引力场,其大小为b=(-G/C~2)(2ГλU/r),其中,Г=1/(1-(U/c)~2)~(1/2) 本文避开四维变换,把引力场同静电场及磁场相对比,从而得出类磁引力和引力坡印亭矢量概念,其结果相同,并以例证说明了类磁引力场中能量守恒问题。

     
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