Dynamically Triangulating Lorentzian Quantum Gravity
Dynamically Triangulating Lorentzian Quantum Gravity
复制标题
动态三角测量洛伦兹量子引力
DOI：
10.1016/s0550-3213(01)00297-8
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
R. Loll
中科院分区：
文献类型：
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作者：
J. Ambjorn;J. Jurkiewicz;R. Loll
关于如何克服引力的富有成果的想法是少之又少的。本文给出了最近引入的一种非微扰引力路径积分的完整描述，它的连续极限在d<4时已经得到了广泛的研究，并得到了有希望的结果。它基于洛伦兹时空的单纯正则化，最重要的是，它拥有一个定义明确的、非微扰的威克旋转。我们提出了一个详细的分析的几何和数学性质的离散模型在d= 3，4。这包括洛伦兹单纯形流形约束的推导，引力作用及其威克旋转。我们定义了一个系统的传输矩阵，并表明它导致一个定义良好的自伴哈密顿。鉴于数值模拟，我们还建议套洛伦兹蒙特卡罗移动。我们证明，以前在欧几里得模型中发现的某些病理阶段的动态三角剖分不能实现在洛伦兹的情况下。
Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d<4, with promising results. It is based on a simplicial regularization of Lorentzian spacetimes and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d=3,4. This includes a derivation of Lorentzian simplicial manifold constraints, the gravitational actions and their Wick rotation. We define a transfer matrix for the system and show that it leads to a well-defined self-adjoint Hamiltonian. In view of numerical simulations, we also suggest sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological phases found previously in Euclidean models of dynamical triangulations cannot be realized in the Lorentzian case.