Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-07-08
Physics
High Energy Physics
High Energy Physics - Theory
36 pages
Scientific paper
In order to extend the spectral action principle to non-compact spaces, we propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. We show that an example is given by the supersymmetric harmonic oscillator which, interestingly, provides two different Dirac operators. This leads to two different representations of the volume form in the Hilbert space, and only their product is the grading operator. The index of the even-to-odd part of each of these Dirac operators is 1. We also compute the spectral action for the corresponding Connes-Lott two-point model. There is an additional harmonic oscillator potential for the Higgs field, whereas the Yang-Mills part is unchanged. The total Higgs potential shows a two-phase structure with smooth transition between them: In the spontaneously broken phase below a critical radius, all fields are massive, with the Higgs field mass slightly smaller than the NCG prediction. In the unbroken phase above the critical radius, gauge fields and fermions are massless, whereas the Higgs field remains massive.
No associations
LandOfFree
Non-compact spectral triples with finite volume does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Non-compact spectral triples with finite volume, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-compact spectral triples with finite volume will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-319927