论文标题
大爆炸和拓扑
Big Bang and Topology
论文作者
论文摘要
在本文中，我们在大爆炸中讨论了宇宙的最初状态。通过使用Freedman的想法，在将四个manifolds嵌入磁盘嵌入定理的证据中，我们将相应的时空描述为引力Instanton。空间空间是一个分形空间（野生嵌入的3速）。然后，我们从这个分形空间构造量子状态。该量子状态是Ocneanu的字符串代数的一部分。琼斯多项式和维滕的拓扑领域理论有联系。使用此链接，我们能够确定物理理论（动作）是Chern-Simons功能。该动作的量规固定决定了时空的叶子以及平滑度的特性。最后，我们确定量子状态的量子对称性为被包络的lie代数$ u_ {q}（sl_ {2}（\ mathbb {c}））$，其中$ q $是团结的第四根。
In this paper we discuss the initial state of the universe at the Big Bang. By using ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as gravitational instanton. The spatial space is a fractal space (wild embedded 3-sphere). Then we construct the quantum state from this fractal space. This quantum state is part of the string algebra of Ocneanu. There is a link to the Jones polynomial and to Witten's topological field theory. Using this link, we are able to determine the physical theory (action) to be the Chern-Simons functional. The gauge fixing of this action determines the foliation of the spacetime and as well the smoothness properties. Finally, we determine the quantum symmetry of the quantum state to be the enveloped Lie algebra $U_{q}(sl_{2}(\mathbb{C}))$ where $q$ is the 4th root of unity.
