有效場論方法於古典廣義相對論之應用

Abstract

在本篇論文中，我們研究由Goldberger 以及Rothstein所提出 的利用古典有效場論(CLEFT)來描述古典相對論理論下的非相 對論物體。利用量子場論的方法，我們可以取得CLEFT的各階 近似。特別的，利用CLEFT我們可以重新導出著名的Einstein -Infeld-Hoffmann (EIH) Lagrangian。在論文的第一部份， 我們回顧一般的Post-Newtonian formalism以及利用此方法導 出EIH equation。在論文的第二部份，我們回顧如何利用費曼 圖得出古典結果，以及將此方法應用在重力場的問題。然後我 們解釋在此CLEFT下的Feynman rules，以及利用費曼圖的方法 導出EIH Lagrangian以及相關結果。

In this thesis we study the classical effective field theory (CLEFT) proposed by Goldberger and Rothstein to describe the dynamics of nonrelativistic extended objects in General Relativity. In this approach the methods of quantum field theory are employed to construct the CLEFT order by order. Especially, we use the CLEFT to re-derive the famous Einstein-Infeld- Hoffmann (EIH) Lagrangian. In the first part of this thesis, we review the conventional Post-Newtonian formalism and the traditional way to obtain EIH equation. In the second part of the thesis, we review the basic ideas how we get classical result via Feynman diagrams and how to apply them to the classical gravity problems. And then we explain the derivations of the Feynman rules in our CLEFT and use the diagrammatic method to derive the EIH Lagrangian and some other results.