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1. Ashtekar Connection

   Linked via "holonomy operator"

   The Holonomy Variable
   A key concept derived from the Ashtekar connection is the holonomy operator, which captures geometric information by parallel transporting the connection around closed loops. This forms the basis of the modern LQG description.
   The holonomy $U(\alpha, p)$ of the connection $A$ along a path $\alpha$ anchored at a point $p$ is defined as: