论文标题
Sobolev空间中的泊松支架：模拟全能式代数
Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra
论文作者
论文摘要
本文的目的是讨论在现场理论中泊松支架计算中出现的许多问题。这对于规范的量化方法特别重要，尤其是循环量子重力。我们通过计算几个示例来说明要点。为了正确理解应如何执行计算，应适当注意相关的分析问题。尽管我们在本文中使用的功能空间可能必须修改以处理特定的物理理论（例如一般相对论），但在这种情况下，我们将提出的许多观点也将是相关的。模拟载体 - 频率代数的具体例子将在某些详细地考虑，并用于得出有关循环量子重力形式主义的一些结论。
The purpose of this paper is to discuss a number of issues that crop up in the computation of Poisson brackets in field theories. This is specially important for the canonical approaches to quantization and, in particular, for loop quantum gravity. We illustrate the main points by working out several examples. Due attention is paid to relevant analytic issues that are unavoidable in order to properly understand how computations should be carried out. Although the functional spaces that we use throughout the paper will likely have to be modified in order to deal with specific physical theories such as general relativity, many of the points that we will raise will also be relevant in that context. The specific example of the mock holonomy-flux algebra will be considered in some detail and used to draw some conclusions regarding the loop quantum gravity formalism.
