Moyal Planes are Spectral Triples

By V. Gayral, J. Gracia-Bond́ıa, B. Iochum, T. Schucker, J. C. Várilly. 2003

237 citations recorded by the source corpus.

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 R2N 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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f64c94e0690867130841dbfe2b742d73f5fce7be

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In Geometry and Topology

1. A. Rennie
2. B. Mesland
3. Frederic Pierre Jean Latrémolière

In Mathematical Physics

1. V. Gayral
2. A. Rennie
3. B. Mesland
4. Frederic Pierre Jean Latrémolière

In Statistical and Nonlinear Physics

1. V. Gayral
2. A. Rennie
3. Frederic Pierre Jean Latrémolière

Citations in the corpus

• The Quantum Gromov-Hausdorff Propinquity (2013, background): “0], we extend the notion of quantum metric space to the locally compactsetting,andwethenshowhowtheMoyalplanecanbeseenasaquantum locally compact metric space by using the spectral triple introduced in [16]. All the examples we have provided share a property which was not a part of Rieffel’s original ”
• Deformation Quantization for Actions of K\"ahlerian Lie Groups. (2011, background): “19], invariance of the K-theory K∗(Aθ,µθ) ≃ K∗(A,µ) [20]...), and many applications have found (for instance in locally compact quantum groups [21], quantum fields theory [11, 12], in spectral triples [15]). In the present article, we investigate the deformation theory of Fr´echet algebras endowed wi”
• Nonunital spectral triples and metric completeness in unbounded KK-theory (2015, background): “ noncommutative geometry. Pertinent examples include quasicentrality [1], Higson’s proof of Kasparov’s technical theorem, [25], and the early approaches to summability for nonunital spectral triples, [23, 44]. In this paper we refine the notion of approximate unit further by looking at differentiable ”