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arXiv · hep-th/0307241

Moyal Planes are Spectral Triples

V. Gayral·J. M. Gracia-Bondía·B. Iochum·T. Schücker·J. C. Varilly
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Abstract

Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces $\R^{2N}$ endowed with Moyal products are intensively investigated. Some physical applications, such as the construction of noncommutative Wick monomials and the computation of the Connes--Lott functional action, are given for these noncommutative hyperplanes.

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V. Gayral, J. M. Gracia-Bondía, B. Iochum, T. Schücker, J. C. Varilly. 2003-10-07. Moyal Planes are Spectral Triples. https://doi.org/10.1007/s00220-004-1057-z

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