Gambini Rodolfo, Pullin Jorge
Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400 Montevideo, Uruguay.
Phys Rev Lett. 2003 Jan 17;90(2):021301. doi: 10.1103/PhysRevLett.90.021301. Epub 2003 Jan 15.
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.
长期以来人们已经认识到，当晶格规范理论公式应用于广义相对论时，与该理论在微分同胚下的不变性相冲突。我们分析离散晶格广义相对论并发展出一种正则形式，它能让人们处理洛伦兹特征时空下的约束理论。晶格的存在引入了一种“动力学规范”固定，这使得理论的量子化在概念上清晰明了，尽管计算过程较为复杂。在我们的方法中，约束的一致代数问题会自动得到解决。该方法在包括拓扑理论在内的其他场论中也能成功应用。一个简单的宇宙学应用展示了大爆炸奇点的量子消除。
