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Spectral Action in Noncommutative Geometry

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 27))

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Abstract

As a desert, we serve a number of open problems connected with the subject matter of the book. Some of them consider the general framework of spectral triples and its possible extensions, while the other are more specific and relate to the properties of the spectral action. The problems are essentially of mathematical nature, though, at least in some cases, the conceptual skeleton strongly depends upon the input from physics. To our mind, the solution to each of these stumbling blocks would advance our understanding of the foundations and implications of the Spectral Action Principle. We therefore cordially invite the Reader to contemplate the list below, both from mathematical and physical perspectives.

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Notes

  1. 1.

    Such a fixed \(C^*\)-algebra can come from physics — as the natural algebra of observables of a given system (see e.g. [42, 49, 61]).

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Authors and Affiliations

  1. Copernicus Center for Interdisciplinary Studies, Kraków, Poland

    Michał Eckstein & Bruno Iochum

  2. Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Kraków, Poland

    Michał Eckstein

  3. National Quantum Information Centre, Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk, Poland

    Michał Eckstein

  4. Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

    Bruno Iochum

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  1. Michał Eckstein
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Correspondence to Michał Eckstein .

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Eckstein, M., Iochum, B. (2018). Open Problems. In: Spectral Action in Noncommutative Geometry. SpringerBriefs in Mathematical Physics, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-94788-4_5

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