TL;DR
This paper explores the properties of extended loops, focusing on their behavior under diffeomorphisms, and develops methods to derive invariants useful in knot theory and quantum gravity.
Contribution
It introduces a new method to obtain analytical diffeomorphism invariants using extended loops, with applications to knot theory and quantum gravity.
Findings
Extended loops have specific behaviors under diffeomorphisms.
A method for analytical expressions of invariants is established.
Applications demonstrate relevance to knot theory and quantum gravity.
Abstract
Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical expressions of diffeomorphism invariants via extended loops are settled. Applications to knot theory and quantum gravity are considered.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics · Quantum Mechanics and Applications