引力磁单极子及低速引力双荷粒子的引力辐射研究

【作者】 全条芬；

【导师】 姚乾凯； 马光文；

【作者基本信息】 郑州大学 ， 粒子物理与原子核物理， 2007， 硕士

【摘要】 为了使有源麦克斯韦方程组具有电磁对偶性，狄拉克提出了磁单极子概念，并进而在量子理论框架内，通过计算得出了电荷量子化条件，即(eg)／((?)c)=1／2n(n=±1，±2，…)。随后，狄拉克又特别强调，磁单极子应该对应着一个半无限长奇异弦(狄拉克弦)的端点，由此便形成了狄拉克磁单极子理论，该理论有助于人们将有源麦克斯韦方程组表达成对偶形式。本文采用双矢势的描述方法，分别讨论了低速和高速双荷粒子的电磁辐射问题。基于此，首先，在弱场近似条件下，通过线性化的引力理论与电磁理论的比较分析发现，爱因斯坦场方程呈现出麦克斯韦方程组的结构形式。据此，我们不仅可以仿照狄拉克理论引入引力磁单极子(引力磁荷)来和质量(引力电荷)相对应，从而使线性化的爱因斯坦场方程也具有对称、完美的结构形式，而且还可以借鉴经典电磁辐射的展开方法——小参数法对引力辐射进行多极展开。其次，根据引力磁荷与引力电荷的对偶性，由变分原理推导出广义的引力场方程组；并且，在弱场近似条件下，该方程组可以自然地恢复到狄拉克—麦克斯韦方程组的形式。这不仅体现出了引力场与电磁场的相似性，同时也表明了上述结果的合理性。此外，我们还推出了低速引力双荷粒子的引力辐射解，并分析和讨论了该解的一般性质，给出了低速运动分别带质量和对偶质量粒子的引力辐射。更多还原

【Abstract】 In order to make the Maxwell’s equations with source more symmetric, Dirac put forward the idea of magnetic poles and gave out the formula of the quantization ofelectricity in quantum mechanics. Then he clearly stated that, each pole should be corresponding to an end of half-infinity string of singularity (i.e. Dirac string), so-called Dirac monopole theory. This theory can help people to express Maxwell’s equations in the dual form.In this paper, by introducing doublet four-dimensional vector potentials, the electromagnetic radiation of the low and high speed moving dyons are discussed respectively. Likewise, first, in the weak field approximation, we find that Einstein’s equations unveil a Maxwell-type structure by comparison of gravitation with electromagnetism. Based on the similarity between Einstein’s equations and the Maxwell’s equations, there should exist the gravitomagnetic monopole (the gravitomagnetic charge) to compare with the mass (the gravitoelectric charge), and the symmetrized form of linearized Einstein’s equations is obtained naturally. In addition, the method of small parameter is used to calculate the multipolar expansion of gravitational radiation in classical situation by analogy with electromagnetism.Second, based on the duality relation between gravitoelectric and gravitomagnetic charges, the generalized gravitational field equations in the presence of the two charges are derived via the variational principle. It is important that, in the weak field approximation, these equations can open up a familiar structure being analogous to the form of Dirac-Maxwell’s equations. Such the situation not only shows the similarity between the gravitational field and the electromagnetic field, but also illustrates the obtained results are reasonable. In addition, the gravitational radiation for low speed moving Gravitational Dyons is given out, and we discuss the property further if the mass and the dual mass exits in space only.更多还原