中文摘要：

研究当存在边界的情形下Dirac场的正则量子化问题.采用文献[1]的观点,将边界条件当作Dirac初级约束.与已有研究不同的是,本文从离散的角度研究此问题.将Dirac场的拉氏量和内在约束进行离散化,并且将离散的边界条件当作初级Dirac约束.因此,从约束的起源来看,这个模型中存在两种不同的约束：一种是由于模型的奇异性而带来的约束,即内在约束;另一种是边界条件.在对此模型进行正则量子化过程中提出一种能够平等地处理内在约束和边界条件的方法.为了证明该方法能够平等地对待这两种起源不同的约束,在计算Dirac括号时分别选取了两个不同的子集合来构造＂中间Dirac括号＂,最后得到了相同的结果.

英文摘要：

The canonical quantization of Dirac field in a finite volume is studied.Following the idea of taking the boundary conditions as primary Dirac constraints,we propose a method to treat both the intrinsic constraints and boundary conditions equally.We shall work in the discrete version and quantize the model canonically.In order to verify our method to treat the intrinsic constraints and boundary conditions on the same footing,we obtain the same results by choosing two different subsets of constraints to construct the intermediate Dirac brackets.