Non-Commutative Geometry, Categories and Quantum Physics
arXiv:0801.2826
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.
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
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Cited by in corpus (11)
- A Horizontal Categorification of Gelfand Duality
- Modular Theory, Non-Commutative Geometry and Quantum Gravity
- A Spectral Theorem for Imprimitivity C*-bimodules
- Categorical Non-commutative Geometry
- Part I, Free Actions of Compact Abelian Groups on C*-Algebras
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- Remarks on Morphisms of Spectral Geometries
- On Strict Higher C*-categories
- Categorical Operator Algebraic Foundations of Relational Quantum Theory
- Applications to quantum gravity from C*-bundles