BCFW 遞迴關係式與玻色開弦中樹圖的散射振幅

Abstract

在本篇論文中，我們將BCFW遞迴關係式的應用從場論散射振幅推廣到弦論。計算弦論的散射振幅困難之處在於需要對無限多個中間物理態 (Intermediate physical state) 做加總。我們將加總的範圍從物理態擴大到全部的 Fock states 解決了這個問題，而且成功地利用此方法計算出四個快子(tachyon)的散射振幅；並更進一步計算出一個任意物理態與三個快子的散射振幅。除此之外，我們了解到利用上述的方法計算散射振幅須要生成函數(generating function)的輔助，且利用路徑積分得到此生成函數的一般結構。

In this thesis, we extend the application of BCFW recursion relation to string tree-level amplitudes. In contrast to the field theory calculation, we encounter the difficulty of summing over all intermediate physical states with infinite tower of mass levels. We develop a method to resolve this difficulty by enlarging the sum over all intermediate physical states to an easier sum over the entire Fock space of string spectrum. The calculation is successfully applied to the 4-tachyon amplitude and then to the cases of one arbitrary higher spin state and 3-tachyon amplitudes. We also figure out a generating function for summing the infinite poles of string spectrum in the BCFW string amplitude calculation. The generic structure of this generating function for higher spin scattering amplitude can be obtained from the standard path integral calculation of string scattering amplitude.