【作者】 代洪霞；

【导师】 李芳昱；

【作者基本信息】 重庆大学 ， 理论物理， 2003， 硕士

【摘要】 对于引力辐射的经典理论和弱场下引力辐射的量子理论各国学者虽然已有很多讨论，但采用较为简洁的经典方法和量子方法讨论引力的多极辐射并给出二者自洽性的研究却并不多见。一般经典方法都涉及到高阶张量的计算，而一般量子方法都要涉及到场算符的计算，这都是很烦琐的。本文采用小参数法作为经典引力辐射的研究方法对引力辐射作多极展开，得到各极引力辐射的一般表达式，并给出了沿任一方向引力辐射的角分布的严格证明，这种展开法在处理四极以上的高阶引力辐射时却可以不涉及更高阶的张量计算。计算结果表明，通常的引力四极辐射的表达式可作为本文的特殊情况而自然得出。另外本文采用简化的量子观点讨论了弱引力场引力辐射的量子表述，计算过程并未涉及大量的算符运算，而且运算结果表明它与经典小参数法得到的相应辐射形式是自洽的。本文用所得到的引力的四极和八极辐射的功率表达式计算了PSR1913+16脉冲双星的多极引力辐射，其四极辐射的总功率数量级为，与已经观测到的间接结果是一致的。另外还预期了相应的八极辐射总功率为。 最后，本文考虑到弱场线性近似条件下引力辐射与电磁辐射的类似，故讨论了引力辐射与电磁辐射之间的对偶关系。更多还原

【Abstract】 The classical theory of gravitational radiation and the quantum theory of it in weak field situation are fully discussed by many authors, but few of them studied on simplifying the methods to deal with the gravitational radiation and on the consistence between corresponding classical and quantum methods. In fact, the calculations are very complex because generally the classical methods have to use high-order tensors and the quantum methods have to use operators.In this paper, the method of small parameter is used to calculate the multipolar expansion of gravitational radiation in classical situation, and the general expression on multipolar gravitational radiation is obtained. Then the angle distribution characters in an arbitrary direction are given. This expansion method can avoid the higher order tensors when dealing with the gravitational radiation higher than quadrupole. Calculated results indicate that the quadrupole radiation expression can be derived out naturally as a specific conclusion of this paper. In addition, using the rough quantum theory of gravity, the quantum form of gravitational radiation in weak field is discussed, which is coincident with the classical results, and the calculation program does not need many operators.Using the expression of the quadrupole and octapole radiation power, the multipole radiation power of a special binary star, PSR1913+16, are estimated. The results show that its whole power of quadrupole radiation is , which is coincident with the observed results, and that the expected whole power of octapole radiation is .Finally, the duality between the gravitational radiation and the electromagnetic radiation is researched because of the similarity between them in the weak field situation.更多还原