在本篇論文中，我們利用路徑積分的方式來探討庫倫作用力下的一維奈米線系統，並且延伸了這套方法來處理有sub-lattice以及有邊界的情形。在這種情形裡某些條件下會有邊界態的存在，利用平均場的方法此一邊界態可以被視為在邊界附近的雜質。利用這套路徑積分的方法，我們可以求出有邊界態時系統的配分函數，並且根據這個配分函數將這個系統波色化。結果發現由於邊界的效應，邊界態的存在並不會對系統有明顯的影響。這個路徑積分的方法有別於一般處理庫倫作用下一維系統的波色化方法，我們也比較了這兩種方法間的關聯。

In this thesis we extend the method of functional integral bosonization to investigate one dimensional systems with sub-lattices and boundaries. In the presence of an edge state, which is treated as an impurity near the edge, the functional form of the partition function can be derived and therefore the system can be properly bosonized. It turns out that due to the boundary effect, as long as the decay length of the edge state is much shorter than the electron-electron correlation length, the edge state has no significant influence to the partition function of this system.

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