Perturbative approach in Loop Quantum Gravity

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Polyrhythmic
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I'm a novice in Loop Quantum Gravity, so please bear with me if this is a trivial question. As far as I know, LQG is usually formulated non-perturbatively, but is there also a perturbative approach in the sense that we use a series expansion in order to calculate vacuum expectation values? Are there Feynman diagrams? Does this even make sense?
 
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Thank you, I will take a look into those papers!