论文标题
部分可观测时空混沌系统的无模型预测
Light ray fluctuations in simplicial quantum gravity
论文作者
论文摘要
长期以来，一项关于光线传播的量子波动的非扰动研究早已迟发。在Lorentzian Simplicial量子重力的理论中，我们计算了经过2,3和4个时空尺寸的对称降低的盒子区域后，测试光线在不同位置降落的概率。发现对于固定的边界条件，当所有耦合常数的绝对值相对较小时，光线波动通常很大。对于固定的耦合常数，随着边界大小的减小，光线波动会首先增加，然后以宇宙常数，Einstein-Hilbert和R-squared项减少。在具有宇宙常数和爱因斯坦 - 希尔伯特（Einstein-Hilbert）术语的3D和4D理论中，随着边界大小的减小，光射线波动却增加了。顺便说一句，在研究2D量子重力时，我们表明，当添加RICCI标量的任意能力时，先前指出的具有宇宙常数和Einstein-Hilbert术语的全局时空二元性也可以。我们通过讨论如何使用光射线波动来获得非扰动洛伦兹量子重力的连续性极限。
A non-perturbative study on the quantum fluctuations of light ray propagation through a quantum region of spacetime is long overdue. Within the theory of Lorentzian simplicial quantum gravity, we compute the probabilities for a test light ray to land at different locations after travelling through a symmetry-reduced box region in 2,3 and 4 spacetime dimensions. It is found that for fixed boundary conditions, light ray fluctuations are generically large when all coupling constants are relatively small in absolute value. For fixed coupling constants, as the boundary size is decreased light ray fluctuations first increase and then decrease in a 2D theory with the cosmological constant, Einstein-Hilbert and R-squared terms. While in 3D and 4D theories with the cosmological constant and Einstein-Hilbert terms, as the boundary size is decreased light ray fluctuations just increase. Incidentally, when studying 2D quantum gravity we show that the global time-space duality with the cosmological constant and Einstein-Hilbert terms noted previously also holds when arbitrary even powers of the Ricci scalar are added. We close by discussing how light ray fluctuations can be used in obtaining the continuum limit of non-perturbative Lorentzian quantum gravity.
