Unification of Commutative Relativity and Noncommutative Quantum Dynamics Via Cyclic Groupoids and Spacetime Fusion Categories

Arturo Tozzi; James F. Peters

doi:10.20944/preprints201809.0021.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 1 September 2018 / Approved: 3 September 2018 / Online: 3 September 2018 (10:51:51 CEST)

The unexploited unification of general relativity and quantum physics is a painstaking issue that prevents physicists to properly understanding the whole of Nature. Here we propose a pure mathematical approach that introduces the problem in terms of group theory. Indeed, we build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses both the theories as subsets, making it possible to join together two of their most dissimilar experimental results, i.e., the commutativity detectable in our macroscopic relativistic world and the noncommutativity detectable in the quantum, microscopic world. This approach, combined with the Connes fusion operator, leads to a mathematical framework useful in the investigation of relativity/quantum mechanics relationships.

Einstein; manifold; Hilbert space; Abelian; dagger category

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Unification of Commutative Relativity and Noncommutative Quantum Dynamics Via Cyclic Groupoids and Spacetime Fusion Categories

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