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Keywords = topological quantum state of the Big Bang

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15 pages, 329 KiB  
Article
Big Bang and Topology
by Torsten Asselmeyer-Maluga, Jerzy Król and Alissa Wilms
Symmetry 2022, 14(9), 1887; https://doi.org/10.3390/sym14091887 - 9 Sep 2022
Cited by 1 | Viewed by 2157
Abstract
In this paper, we discuss the initial state of the universe at the Big Bang. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as a gravitational instanton. The spatial space [...] Read more.
In this paper, we discuss the initial state of the universe at the Big Bang. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as a 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 between the Jones polynomial and Witten’s topological field theory. Using this link, we are able to determine the physical theory (action) as the Chern–Simons functional. The gauge fixing of this action determines the foliation of the spacetime and the smoothness properties. Finally, we determine the quantum symmetry of the quantum state to be the enveloped Lie algebra Uq(sl2(C)), where q is the fourth root of unity. Full article
(This article belongs to the Special Issue Symmetry Principles in Quantum Systems II)
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