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arXiv · 2207.03345

Non-commutative Geometry from Perturbative Quantum Gravity

Markus Fröb·Albert Much·Kyriakos Papadopoulos
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Abstract

Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where perturbative quantum gravity provides a predictive framework? Moreover, is it necessary to introduce non-commutativity by hand, or does it arise through quantum-gravitational effects? We show that the first question can be answered in the affirmative, and the second one in the negative: perturbative quantum gravity predicts non-commutativity at the Planck scale, once one clarifies the structure of observables in the quantum theory.

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Markus Fröb, Albert Much, Kyriakos Papadopoulos. 2022-07-06. Non-commutative Geometry from Perturbative Quantum Gravity. https://doi.org/10.1103/physrevd.107.064041

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