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The Dwelling of the Spectral Action

  • Michał EcksteinEmail author
  • Bruno Iochum
Chapter
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 27)

Abstract

The natural habitat of the spectral action is Connes’ noncommutative geometry. Therefore, it is indispensable to lay out its rudiments encoded in the notion of a spectral triple. We will, however, exclusively focus on the aspects of the structure, which are relevant for the spectral action computations. These include i.a. the abstract pseudodifferential calculus, the dimension spectrum and noncommutative integrals, based on both the Wodzicki residue and the Dixmier trace.

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Copernicus Center for Interdisciplinary StudiesKrakówPoland
  2. 2.Faculty of Physics, Astronomy and Applied Computer ScienceJagiellonian UniversityKrakówPoland
  3. 3.National Quantum Information Centre, Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and InformaticsUniversity of GdańskGdańskPoland
  4. 4.Aix-Marseille Univ, Université de Toulon, CNRS, CPTMarseilleFrance

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