Noncommutative geometry from perturbative quantum gravity
Markus B. Fröb, Albert Much, Kyriakos Papadopoulos
Abstract
Trying to connect a fundamentally noncommutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are noncommutative geometrical effects already present in the regime where perturbative quantum gravity provides a predictive framework? Moreover, is it necessary to introduce noncommutativity 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 noncommutativity at the Planck scale, once one clarifies the structure of observables in the quantum theory.
Topics & Concepts
Noncommutative geometryPhysicsQuantum gravityNoncommutative quantum field theorySpin foamQuantum differential calculusQuantum geometryLoop quantum gravityEuclidean quantum gravityHořava–Lifshitz gravityTheoretical physicsGravitationClassical mechanicsQuantum spacetimeQuantumQuantum mechanicsMathematical physicsQuantum processQuantum dynamicsNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsQuantum Electrodynamics and Casimir Effect