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arXiv 2209.08056gr-qchep-thmath-phmath.MP
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大爆炸与拓扑学

Big Bang and Topology

Torsten Asselmeyer-Maluga, Jerzy Krol, Alissa Wilms

摘要:

在本文中,我们讨论了宇宙大爆炸时的初始状态。利用Freedman在四维流形圆盘嵌入定理证明中的思想,我们将相应的时空描述为引力瞬子。空间是一个分形空间(野生嵌入3球)。然后我们从这个分形空间中构造出量子态。这个量子态是奥克内亚努弦代数的一部分。有一个链接到琼斯多项式和威滕的拓扑场论。使用这个链接,我们能够确定物理理论(作用)是陈-西蒙斯泛函。这个作用量的规范固定决定了时空的叶理和光滑性。最后,我们确定量子态的量子对称性为包络李代数$U_{q}(sl_{2}(\mathbb{C}))$,其中$q$是单位的4次方根。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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