English

The Spectral Action Principle

High Energy Physics - Theory 2009-07-09 v1

Abstract

We propose a new action principle to be associated with a noncommutative space (\Ac,\Hc,D)(\Ac ,\Hc ,D). The universal formula for the spectral action is (ψ,Dψ)+\Trace(χ(D/(\psi ,D\psi) + \Trace (\chi (D / \Lb))\Lb)) where ψ\psi is a spinor on the Hilbert space, \Lb\Lb is a scale and χ\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)SU(5) as well as the Higgs self-coupling, to be taken at a fixed high energy scale.

Keywords

Cite

@article{arxiv.hep-th/9606001,
  title  = {The Spectral Action Principle},
  author = {Ali H. Chamseddine and Alain Connes},
  journal= {arXiv preprint arXiv:hep-th/9606001},
  year   = {2009}
}

Comments

27 pages, Tex file