Kinematical Uniqueness of Loop Quantum Gravity
Christian Fleischhack
TL;DR
This paper reviews the unique kinematical structures in loop quantum gravity, focusing on the holonomy-flux and Weyl algebras and their diffeomorphism-invariant representations.
Contribution
It provides a comprehensive overview of the uniqueness results for the kinematical framework in loop quantum gravity, highlighting the mathematical structures involved.
Findings
Holonomy-flux algebra has a unique diffeomorphism-invariant representation.
Weyl algebra also admits a unique diffeomorphism-invariant representation.
The review clarifies the foundational mathematical structures of loop quantum gravity.
Abstract
We review uniqueness results for the kinematical part of loop quantum gravity. After sketching the general loop formalism, the holonomy-flux and the Weyl algebras are introduced. In both cases, then, diffeomorphism invariant representations are described.
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