量子宇宙学中恢复时间的WKB方法：预测和缩短
WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
摘要：
在这篇综述中，我们分析了不同方面的可能性，分离的引力物质系统的一部分，生活接近准经典状态和一个“小”量子子集。所考虑的方法都是依赖于一个WKB展开的动力学的序参量和自然竞技场组成的Bianchi宇宙minisuperspace。我们首先讨论如何，限制WKB展开到一阶近似，它是可能的恢复量子子系统的薛定谔方程写在经典的引力背景。我们给出了量子子系统在Bianchi IX模型的“角”配置中的一些应用，确定了两个各向异性自由度中较小的一个中的量子变量。最令人惊讶的结果是，当这种情况在时间上向后外推时，有可能得到一个非奇异的比安奇九世宇宙学。我们还提供了一些基本的提示，这个结果的推广到一般的宇宙学解决方案。在评论的最后一部分，我们考虑了相同的计划，以下一阶近似确定量子子集的物质变量。本文讨论了量子引力对量子场论的修正的非幺正形态学这一非常基本的问题，并讨论了一些建议的修正。我们分析了最近提出的通过固定一个参考系来构造时间的建议，而不是通过一个经典的引力变量来构造时间依赖性。该方案可以通过引入所谓的“运动学作用”以及通过众所周知的Kuchar-Torre公式来实现。在这两种情况下，薛定谔方程，修正为量子引力修正，具有相同的形态，我们提供了一个宇宙学实现的模型，阐明其可能的预测。
英文摘要：
In this review, we analyse different aspects concerning the possibility to separate a gravity-matter system into a part which lives close to a quasi-classical state and a "small" quantum subset. The considered approaches are all relying on a WKB expansion of the dynamics by an order parameter and the natural arena consists of the Bianchi universe minisuperspace. We first discuss how, limiting the WKB expansion to the first order of approximation, it is possible to recover for the quantum subsystem a Schrödinger equation as written on the classical gravitational background. We give some applications for the quantum subsystem in the "corner" configuration of the Bianchi IX model, identifying the quantum variable in the small one of the two anisotropy degrees of freedom. The most surprising result is the possibility to get a non-singular Bianchi IX cosmology when the scenario is extrapolated backwards in time. We also provide some basic hints on the extension of this result to the generic cosmological solution. In the last part of the review, we consider the same scheme to the next order of approximation identifying the quantum subset as made of matter variables only. We deal with the very fundamental problem of non-unitary morphology of the quantum gravity corrections to quantum field theory discussing some proposed reformulations. Instead of constructing the time dependence via that one of the classical gravitational variables on the label time, we analyse a recent proposal to construct time by fixing a reference frame. This scheme can be reached both introducing the so-called "kinematical action", as well as by the well-known Kuchar-Torre formulation. In both cases, the Schrödinger equation, amended for quantum gravity corrections, has the same morphology and we provide a cosmological implementation of the model, to elucidate its possible predictions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
