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arXiv · 0801.2826

Non-Commutative Geometry, Categories and Quantum Physics

Paolo Bertozzini·Roberto Conti·Wicharn Lewkeeratiyutkul
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Abstract

After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of A.Connes' non-commutative geometry: morphisms/categories of spectral triples, categorification of Gel'fand duality. We conclude with a summary of the expected applications of "categorical non-commutative geometry" to structural questions in relativistic quantum physics: (hyper)covariance, quantum space-time, (algebraic) quantum gravity.

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Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul. 2011-12-27. Non-Commutative Geometry, Categories and Quantum Physics. https://arxiv.org/abs/0801.2826

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