Moyal Planes are Spectral Triples
High Energy Physics - Theory
2016-08-16 v3 Operator Algebras
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 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.
Cite
@article{arxiv.hep-th/0307241,
title = {Moyal Planes are Spectral Triples},
author = {V. Gayral and J. M. Gracia-Bondía and B. Iochum and T. Schücker and J. C. Varilly},
journal= {arXiv preprint arXiv:hep-th/0307241},
year = {2016}
}
Comments
Latex, 54 pages. Version 3 with Moyal-Wick section updated