Abstract
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.