The spectral action for Moyal planes

Victor Gayral; Bruno Iochum

doi:10.1063/1.1855401

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arXiv · hep-th/0402147

The spectral action for Moyal planes

Victor Gayral·Bruno Iochum

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Abstract

Extending a result of D.V. Vassilevich, we obtain the asymptotic expansion for the trace of a "spatially" regularized heat operator associated with a generalized Laplacian defined with integral Moyal products. The Moyal hyperplanes corresponding to any skewsymmetric matrix $Θ$ being spectral triples, the spectral action introduced in noncommutative geometry by A. Chamseddine and A. Connes is computed. This result generalizes the Connes-Lott action previously computed by Gayral for symplectic $Θ$.

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Victor Gayral, Bruno Iochum. 2004-03-17. The spectral action for Moyal planes. https://doi.org/10.1063/1.1855401

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