【作者】 何文丽；

【导师】 赵柳；

【作者基本信息】 西北大学 ， 理论物理， 2003， 博士

【摘要】 边界问题一直是世界范围内数学和物理科学领域中人们集中关注的重要问题之一。尤其是边界理论的量子化问题，因其在物理学中的重要性而形成了十分活跃的研究方向。尽管如此，对于如何实现带边界理论的量子化，至今仍没有一套系统而完整的解决方案。因为当一个理论中出现边界时，其原来标准的正则Poisson结构往往会与边界条件不自洽，而本文正是考虑到这一点，才试探性地提出了一种处理这种不自洽性问题的新方法。简单来说，我们的新处理方法是根据带边界理论的因果律及局域性分析，通过对该理论原来无边界情形下标准的正则Poisson结构进行适当修正，从而使其最终与边界条件相自治的。 本文共分为五章。由于边界条件通常是被当作约束来处理的，所以我们在第一章首先对处理约束系统量子化问题常用的Dirac方法作了简单的回顾。接着，我们试图利用Dirac方法对带有边界条件的理论进行量子化。结果发现，在用Dirac方法来处理具有这类特殊边界约束的系统的量子化问题时，总是存在着不可避免的闲难或弊端。这样，分析并提出解决这一问题的更为恰当的新方法就成为我们后面章节中的主要研究任务。 在第二章，我们对D+1维带边界的的质量单标量场的Poisson结构进行了修正，并在此基础上详细讨论了D+1维有质量单标量场在边界相互作用势时的量子化，同时还给出了具有边界相互作用势的2+1维有质量单标量在半平面上的自洽的Poisson结构的基本形式。 第三章我们分别讨论了端点附着于D-膜上的开弦在常的Neveu-Schwarz背景场下的量子化及在非常背景场下的自治的Poisson结构。并且，我们通过对结果的分析指出，D-膜上的场论究竟是对易的还是非对易的，主要取决于观测者所选择的新的自洽的Poisson结构的具体形式。 第四章是为了进一步说明我们这一新方法的可行性，又分别对限制于半直线上或附加了可积边界项的O(N)非线性σ模型、经典非线性σ模型和Gross-Neveu模型的自洽的Poisson结构及量子化进行了简单讨论。第五章则是对本文的总结及对下一步研究工作的展望。更多还原

【Abstract】 The study of boundary problems continues to be one of the subjects of intensive research in the mathematical and physical sciences worldwide. In particular, because of its significance in physical science, the quantization of a theory with boundary has become a quite active research direction. However, a systematical and complete solution on how to accomplish the quantization for a theory with boundary is still missing, since the appearance of a boundary will generally make the standard canonical Poisson structure inconsistent with the boundary condition. In this thesis, we propose a new method to treat the inconsistency problem. The new treatment is a modified definition of the naive Poisson structure according to the analysis of the causality and locality of the theory in the presence of a boundary condition.This thesis is divided into five chapters. Since the boundary conditions are usually regarded as constraints, we first give a brief review on the usual method for the Hamil-tonian description of physical system with constraints, i.e. the Dirac method. The special class of constraints which appears in the form of boundary conditions is then considered within the framework of Dirac method and some unavoidable problems or shortcommings of the Dirac method in treating boundary constraints are pointed out. This constitutes Chapter One. Now that the Dirac procedure is not quite appreciated to quantize the boundary model under consideration, to search for a new method to solve this problem becomes our main task in the forthcoming chapters.In Chapter Two, the quantization for D + 1-dimensional massive single scalar field with boundary is considered. Especially, the quantization of D + 1-dimensional massive single scalar field with boundary interaction potential and the proper Poisson structure of 24- 1-dimensional massive single scalar field with boundary interaction potential VB=1/2 on a half plane are discussed in great detail.In Chapter Three, consistent boundary Poisson structures for an open string ending on D-branes with a constant and non-constant background Neveu-Schwarz B fields are considered respectively, and rhe results indicate that whether field theories livingon D-branes are commutative or noncommutative depends on which consistent Poisson structure the observer chooses.Furthermore, to show the feasibility of our new approach, we briefly discuss the quantization of O(N) nonlinear sigma model, classical nonlinear sigma model and Gross-Neveu model which are constrained on a half line or supplemented by integrable boundary terms in Chapter Four. Chapter Five contains some concluding remarks and outlines of several problems for the future research.更多还原