物理学报Issue(10)：1-7,7.DOI:10.7498/aps.64.100301
有限空间中经典场的正则量子化∗
Canonical quantization of classical fields in finite volume
摘要
Abstract
We study the problem of canonical quantization of classical scalar and Dirac field theories in the finite volumes respectively in this paper. Unlike previous studies, we work in a completely discrete version. We discretize both the space and time variables in variable steps and use the difference discrete variational principle with variable steps to obtain the equations of motion and boundary conditions as well as the conservation of energy in discrete form. For the case of classical scalar field, the quantization procedure is simpler since it does not contain any intrinsic constraint. We take the boundary conditions as primary Dirac constraints and use the Dirac theory to construct Dirac brackets directly. However, for the case of classical Dirac field in a finite volume, things are complex since, besides boundary conditions, it contains intrinsic constraints which are introduced by the singularity of the Lagrangian. Furthermore, these two kinds of constraints are entangled at the spatial boundaries. In order to simplify the process of calculation, we calculate the final Dirac brackets in two steps. We calculate the intermediate Dirac brackets by using intrinsic constraints. And then, we obtain the final Dirac brackets by bracketing the boundary conditions. Our studies show that we can not only construct well-defined Dirac brackets at each discrete space-time lattice but also keep the conservation of energy discretely at the same time.关键词
正则量子化/边界条件/Dirac约束/Dirac括号Key words
canonical quantization/boundary conditions/Dirac constraints/Dirac brackets引用本文复制引用
刘波,王青,李永明,隆正文..有限空间中经典场的正则量子化∗[J].物理学报,2015,(10):1-7,7.基金项目
国家自然科学基金(批准号10865003)资助的课题．* Project supported by National Natural Science Foundation of China (Grant No.10865003) （批准号10865003）
