Spectral geometry of the Moyal plane with harmonic propagation

Details Spectral geometry of the Moyal plane with harmonic propagation Spectral geometry of the Moyal plane with harmonic propagation

2011-08-10

arxiv.org/abs/1108.2184v1

Mathematics

Operator Algebras

37 pages

Scientific paper

We construct a `non-unital spectral triple of finite volume' out of the Moyal product and a differential square root of the harmonic oscillator Hamiltonian. We find that the spectral dimension of this triple is d but the KO-dimension is 2d. We add another Connes-Lott copy and compute the spectral action of the corresponding U(1)-Yang-Mills-Higgs model. We find that the `covariant coordinate' involving the gauge field combines with the Higgs field to a unified potential, yielding a deep unification of discrete and continuous parts of the geometry.

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