Fabiano, Giuseppe (2024) Spacetime noncommutativity and cold atoms. [Tesi di dottorato]

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Heuristic arguments in quantum gravity research suggest that there should be a fundamental limit to the localization of particles and fields. Several quantum gravity theories incorporating this feature can be effectively described by means of noncommutative geometry, in which smooth, classical coordinates are promoted to operators satisfying non-trivial commutation relations. This thesis contains both theoretical and phenomenological results based on the spacetime noncommutativity hypothesis. In the first part, I develop the relativistic theory of a free complex scalar field on the so-called "lightlike kappa-Minkowski" noncommutative spacetime. I analyze its discrete symmetries and construct well-defined multiparticle states, finding deviations from the Pauli exclusion principle, which could be potentially observable in underground experiments. I then proceed to discuss the role of observers and reference frames when spacetime symmetries are deformed in a way that is compatible with spacetime noncommutativity. In this perspective, I also investigate the fate of the Noether theorem, emphasizing a fundamental connection between conserved charges and dynamics. The last part of the thesis is devoted to quantum gravity phenomenology inspired by spacetime noncommutativity. In particular, I show that the "lightlike kappa-Minkowski" model suggests a deformation of particle kinematics in which an infrared ultraviolet mixing mechanism occurs. The introduction of the ultraviolet noncommutativity scale brings about corrections in the dispersion relation of particles which become dominant in the infrared regime. I thus discuss potential observable effects in cold atom interferometry experiments due to this mechanism.

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