Coordinate time dependence in Quantum Gravity
Coordinate time dependence in Quantum Gravity
复制标题
协调量子引力中的时间依赖性
DOI：
10.1103/physrevd.70.124022
复制
发表时间：
2004
影响因子：
5
通讯作者：
Aureliano Skirzewski
中科院分区：
文献类型：
--
作者：
M. Bojowald;Parampreet Singh;Aureliano Skirzewski
直观的经典时空图景在量子引力中被分解，这使得半经典技术的比较和发展变得相当复杂。使用群平均方法的成分来解决约束，人们仍然可以将经典的坐标时间引入量子理论，并用它来研究从离散量子演化中产生半经典连续描述的方式。应用这一技术检验了环状宇宙学的有效经典方程及其对暴涨和反弹的影响，结果表明，有效的半经典理论与量子描述即使在短尺度下也是一致的。因此，在非均匀模型或完整理论中更是如此。根据前面的讨论，一个悬而未决的问题是，在哪里有效的经典方程作为差分方程的行为的良好近似是有意义的，以及在哪里必须考虑额外的修正项。这个问题可以通过直接比较有效的半经典描述(由常微分方程式给出)和基本的离散量子演化由差分方程式(这些差分方程式甚至可能是部分的，取决于物质场的数目)来回答。但是，由于常微分方程组与离散微分方程组有很大的不同，它们的解不能直接比较。为此，我们首先必须从差分方程解中提取适当的数据，通常是通过取期望值，然后我们将其与经典理论或经过进一步修正的理论进行比较。(在这一点上，人们必须区分由于选择如何提取半经典数据而产生的歧义和与纯经典行为的直接偏差。如何解决这一问题将在稍后讨论。)这样，人们就可以看到是否会出现新的影响，或者在什么范围内人们可以信任一个有或没有某些修正项的有效的经典方程。
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one can nevertheless introduce a classical coordinate time into the quantum theory, and use it to investigate the way a semiclassical continuous description emerges from discrete quantum evolution. Applying this technique to test effective classical equations of loop cosmology and their implications for inflation and bounces, we show that the effective semiclassical theory is in good agreement with the quantum description even at short scales. so even more in inhomogeneous models or the full theory. In light of the previous discussion an open question is where exactly an effective classical equation makes sense as a good approximation to the behavior of the difference equation, and where additional correction terms have to be taken into account. This question can be answered by a direct comparison of effective semiclassical descriptions, given by ordinary dif- ferential equations, with the underlying discrete quantum evolution governed by difference equations (these differ- ence equations may even be partial depending on the number of matter fields). However, since an ordinary dif- ferential equation is quite different from a discrete differ- ence equation, their solutions cannot be compared directly. For such a purpose we first have to extract appropriate data from solutions of the difference equation, usually by taking expectation values, which we then compare to the classical theory or one with further corrections. (At this point one has to distinguish between ambiguities resulting from choosing how to extract the semiclassical data and outright deviations from the purely classical behavior. How this can be disentangled will be discussed later.) In this way one can see if new effects arise or in which range one can trust an effective classical equation with or without certain correc- tion terms.