Noncommutative Geometry, the Spectral Standpoint. Connes, A. In New Spaces in Physics: Formal and Conceptual Reflections, pages 23–84. Cambridge University Press, 2021. Publisher: Cambridge University Pressabstract bibtex We update our Year 2000 account of Noncommutative Geometry in [65]. There, we described the following basic features of the subject: The natural “time evolution" that makes noncommutative spaces dynamical from their measure theory. The new calculus which is based on operators in Hilbert space, the Dixmier trace and the Wodzicki residue. The spectral geometric paradigm which extends the Riemannian paradigm to the noncommutative world and gives a new tool to understand the forces of nature as pure gravity on a more involved geometric structure mixture of continuum with the discrete.
@incollection{connes_noncommutative_2021,
title = {Noncommutative {Geometry}, the {Spectral} {Standpoint}},
isbn = {978-1-108-84820-6 1-108-84820-6},
abstract = {We update our Year 2000 account of Noncommutative Geometry in [65]. There, we described the following basic features of the subject: The natural “time evolution" that makes noncommutative spaces dynamical from their measure theory. The new calculus which is based on operators in Hilbert space, the Dixmier trace and the Wodzicki residue. The spectral geometric paradigm which extends the Riemannian paradigm to the noncommutative world and gives a new tool to understand the forces of nature as pure gravity on a more involved geometric structure mixture of continuum with the discrete.},
booktitle = {New {Spaces} in {Physics}: {Formal} and {Conceptual} {Reflections}},
publisher = {Cambridge University Press},
author = {Connes, Alain},
year = {2021},
note = {Publisher: Cambridge University Press},
pages = {23--84},
}
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