时间与时间统计量子几何动力学
Time and a Temporally Statistical Quantum Geometrodynamics
摘要：
本文阐述了作者最近的工作（arXiv：1001.3382 [hep-th]，arXiv：1005.5430 [cond-mat.dis-nn]，arXiv：1212.4956 [quant-ph]），在量子几何动力学的时间统计描述的框架内，对M理论和量子力学观测者进行建模，包括基于量子引力正则理论的测量过程。在这篇论文中，我们讨论了几个基本的时间问题：正则量子引力中的无时间问题;态约化的物理起源;以及时间反演对称性破缺。我们首先模拟观察者，并考虑通过调用时间重参数化对称性破缺的量子力学世界中的观察者看到的无时间的问题。接下来，我们使用IIB型弦论中规范化和仿射化的S-对偶对称模型，构造了隐时间变量理论，作为时间的统计理论，并解释了使用它的状态约简的物理起源。最后，通过将时间重参数化对称性扩展到所有的时间隐变量，我们将时间反演对称性破缺的问题视为这种扩展的时间重新参数化对称性的自发破缺。研究了酉时变过程的分类以及利用导出范畴的语言对酉和非酉时变过程的几何化。
英文摘要：
This paper is an exposition of the author's recent work (arXiv:1001.3382 [hep-th], arXiv:1005.5430 [cond-mat.dis-nn], arXiv:1212.4956 [quant-ph]) on modeling M-theory vacua and quantum mechanical observers in the framework of a temporally statistical description of quantum geometrodynamics, including measurement processes based on the canonical theory of quantum gravity. In this paper we deal with several fundamental issues of time: the time-less problem in canonical quantum gravity; the physical origin of state reductions; and time-reversal symmetry breaking. We first model the observers and consider the time-less problem by invoking the time reparametrization symmetry breaking in the quantum mechanical world as seen by the observers. We next construct the hidden time variable theory, using a model of the gauged and affinized S-duality symmetry in type IIB string theory, as the statistical theory of time and explain the physical origin of state reductions using it. Finally, by the extension of the time reparametrization symmetry to all of the temporal hidden variables, we treat the issue of time reversal symmetry breaking as the spontaneous breaking of this extended time reparametrization symmetry. The classification of unitary time-dependent processes and the geometrizations of unitary and non-unitary time evolutions using the language of the derived category are also investigated.
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