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Fluctuations of the Spectral Action

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

Abstract

As we have learned in Sect.  1.6 a given spectral triple \((\mathscr {A,H,D})\) ought to be considered as a representative of the entire family of triples \((\mathscr {A},\mathscr {H},\mathscr {D}_{\mathbb {A}})\), which yield equivalent geometries. It is therefore of utmost importance to understand how the spectral action is affected by the fluctuations of geometry. We explore the meromorphic structure of the fluctuated zeta function and, for regular spectral triples with simple dimension spectra, we provide a few formulae for the noncommutative integrals. Finally, we sketch the method of operator perturbations.

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Copyright information

© 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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