标题： 动态三角化，量子引力的入口？ 显示英文标题

标题： Dynamical Triangulations, a Gateway to Quantum Gravity ?

摘要： 我们展示如何通过动态三角剖分，将欧几里得二维量子引力表述为普通统计系统的尺度极限，这可以看作是度量等价类空间的离散化。 存在尺度关系，临界指数具有简单的几何解释。 可以计算哈特尔-霍金波函数以及依赖于测地线距离的重参数化不变相关函数。 离散化方法在更高维时空中也有意义。 尽管在更高维情况下仍缺乏解析解，但数值研究揭示了有趣的结构，并允许识别一个固定点，在此我们可以希望定义一个真正的四维量子引力非微扰理论。 显示英文摘要

摘要： We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of equivalence classes of metrics. Scaling relations exist and the critical exponents have simple geometric interpretations. Hartle-Hawkings wave functionals as well as reparametrization invariant correlation functions which depend on the geodesic distance can be calculated. The discretized approach makes sense even in higher dimensional space-time. Although analytic solutions are still missing in the higher dimensional case, numerical studies reveal an interesting structure and allow the identification of a fixed point where we can hope to define a genuine non-perturbative theory of four-dimensional quantum gravity.