The Spectral Action Principle

Details The Spectral Action Principle The Spectral Action Principle

1996-06-03

arxiv.org/abs/hep-th/9606001v1

Commun.Math.Phys.186:731-750,1997

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, Tex file

Scientific paper

10.1007/s002200050126

We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space, $\Lb$ is a scale and $\chi$ a positive function. When this principle is applied to the noncommutative space defined by the spectrum of the standard model one obtains the standard model action coupled to Einstein plus Weyl gravity. There are relations between the gauge coupling constants identical to those of $SU(5)$ as well as the Higgs self-coupling, to be taken at a fixed high energy scale.

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