標題: N相黎曼面上的路徑積分及微分方程上之應用
Path Integrals on Riemann Surfaces of Genus N and Its Applications on Differential Equations
作者: 施建興
Shih, Chien-Hsin
李榮耀
Lee, Jong-Eao
應用數學系所
關鍵字: 黎曼空間;代數結構;幾何結構;路徑積分;Riemann Surface;algebraic structure;geometry structure;path integrals
公開日期: 2010
摘要: 假設 P(u) 是一個 u 的多項式函數且 f(u)=Sqrt{P(u)}。 在 complex plane 上 f 是一個多值函數。在 extended complex plane 上我們利用適合的 cut-structure 建立 f 的 Riemann surface R 。則 f 是一個定義在 R 上的單值函數。接著我們在 f 的代數結構上面做積分的運算。特別地,我們主要針對兩種特別的路徑來積分,分別為 a-cycle 及 b-cycle 。運用 principle of deformation of paths 來計算這些積分。此外,我們將以上的方法應用在微分方程上。
Let P(u) be a polynomial of u and let f(u)=Sqrt{P(u)}. f is a 2-valued function defined on the complex plane C. We construct the Riemann surface R by a proper cut-structure on the extended complex plane. Then f is a single-valued function on R. Then we do evaluations of path integrals on R with its algebraic structure for f. In particular, we evaluate integrals along two special paths, a-cycle and b-cycle, respectively. We apply the principle of deformation of paths to evaluate those integrals. Furthermore, we apply the above argument to differential equations.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT079622529
http://hdl.handle.net/11536/42516
Appears in Collections:Thesis


Files in This Item:

  1. 252901.pdf