The Einstein-Hilbert Action as a Spectral Action
Bernd Ammann and Christian Bär

The Einstein-Hilbert Action as a Spectral Action (The links on this webpage are currently deaktivated, as they intersect with current exercise questions) (.pdf , .ps oder .ps.gz),
Vortrag auf der Arbeitstagung "Das Standardmodell der Elementarteilchenphysik unter mathematisch-geometrischem Aspekt", Hesselberg 1999,

erschienen im Tagungsband: F. Scheck, H. Upmeiner (ed.),
Noncommutative Geometry and the Standard Model of Elementary Particle Physics,
Springer Lecture Notes in Physics 596, 2002.


Exposition of heat asymptotics for generalized Laplace operators, Weyl's asymptotics for the eigenvalues, variation of the total scalar curvature functional (Einstein-Hilbert action), and of a theorem by Kalau/Walze and Kastler independently relating the second heat coefficient to the Wodzicki residue.

The article is part of the Proceedings at Hesselberg 1999.

Mathematics Subject Classification

58G11, 58G15, 58G18


Laplace operator, Dirac operator, heat equation, asymptotic solution, scalar curvature functional, Wodzicki residue

Bernd Ammann, 28.4.1999