arXiv 0801.28262008-01math.OAgr-qchep-thmath.CTquant-ph

Non-Commutative Geometry, Categories and Quantum Physics

Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul

备注：: Survey paper, 70 pages, AMS-LaTeX2e, results unchanged, considerably expanded version of the published paper (only for the arXiv repository), bibliography updated to October 2009, significant improvements and expansions in several sections, added appendix with selected recent references
发表信息：: East-West Journal of Mathematics "Contributions in Mathematics and Applications II" Special Volume 2007, 213-259 (2008)

英文摘要：

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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