有效場論方法於古典廣義相對論之應用

The Application of the Effective Field Theory Method to Classical General Relativity

林韋辰(Wei-Chen Lin)

指導教授 ： 高涌泉

國立臺灣大學/理學院/物理研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02070

摘要

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。

關鍵字

廣義相對論 ； 古典有效場論 ； 後牛頓近似

並列摘要

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.

並列關鍵字

General Relativity ； classical effective field theory ； The post-Newtonian Approximation

參考文獻

[1] L. Blanchet, “On the two-body problem in general relativity,” arXiv:gr-qc/0108086.

[2] Einstein A., Infeld L., Hoffmann B., Ann. Math. 39 (1938) 65.

Einstein A., Infeld L., Ann. Math. 41 (1940) 797.

Einstein A., Infeld L., Can. J. Math. 1 (1949) 209.

[3] W. D. Goldberger and I. Z. Rothstein, “An effective field theory of gravity for extended objects,” Phys. Rev. D 73 (2006) 104029 [arXiv:hep-th/0409156].