论文标题
规范的量子重力，建设性QFT和重量级化
Canonical Quantum Gravity, Constructive QFT and Renormalisation
论文作者
论文摘要
近几十年来，量子重力的规范方法已成为牢固的数学基础。但是，由于重力相互作用的极其非物质特征，也可以严格定义量子动力学，相应的Wheeler-Dewitt操作员有价值的分布受到定量歧义，需要固定。 在最近的一系列作品中，我们采用了建设性量子场理论的方法来解决这些歧义。建设性QFT将量子字段用于随机变量，并以量子统计物理学的语言逐渐衡量理论。与规范公式的连接是通过Osterwalder-Schrader重建进行的。在量子统计中众所周知，可以使用重态化固定措施中的相应歧义。因此，相关的重量法流量可用于定义规范的重态化程序。 本文的目的是审查和进一步发展这些想法，并将它们与早期和并行计划紧密相关的背景。
The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the gravitational interaction, the corresponding Wheeler-DeWitt operator valued distribution suffers from quantisation ambiguities that need to be fixed. In a very recent series of works we have employed methods from constructive quantum field theory in order to address those ambiguities. Constructive QFT trades quantum fields for random variables and measures thereby phrasing the theory in the language of quantum statistical physics. The connection to the canonical formulation is made via Osterwalder-Schrader reconstruction. It is well known in quantum statistics that the corresponding ambiguities in measures can be fixed using renormalisation. The associated renormalisation flow can thus be used to define a canonical renormalisation programme. The purpose of this article is to review and further develop these ideas and to put them into context with closely related earlier and parallel programmes.
