Year: 2017
Type: preprint
Abstract: A hyperlink is a finite set of non-intersecting simple closed curves in $\mathbb{R} \times \mathbb{R}^3$. We compute the Wilson Loop observable using a path integral with an Einstein-Hilbert action. Using axial-gauge fixing, we can write this path integral as the limit of a sequence of Chern-Simons integrals, studied earlier in our previous work on the Chern-Simons path integrals in $\mathbb{R}^3$. We will show that the Wilson Loop observable can be computed from a link diagram of a hyperlink, projected on a plane. Only crossings in the diagram will contribute to the path integral. Furthermore, we will show that it is invariant under an equivalence relation defined on the set of hyperlinks.
Source: arXiv (Cornell University)
Author: Lim, Adrian P. C.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2572079336