Spectral geometry of the Moyal plane with harmonic propagation

DOI10.4171/JNCG/140zbMath1295.46054arXiv1108.2184MaRDI QIDQ2438303

Raimar Wulkenhaar, Victor Gayral

Publication date: 11 March 2014

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2184

zbMATH Keywords

heat kernel techniquesnoncommutative differential geometryMoyal deformationnon-unital spectral triplesquantum theory: noncommutative geometry methods

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Noncommutative geometry methods in quantum field theory (81T75)

Related Items

Noncommutative field theories on \( \mathbb{R}_{\lambda}^3 \): towards UV/IR mixing freedom, Closed star product on noncommutative \(\mathbb R^{3}\) and scalar field dynamics, Exact partition functions for gauge theories on \(\mathbb{R}_\lambda^3\), Indefinite Kasparov modules and pseudo-Riemannian manifolds, Matrix geometries emergent from a point, 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory, Integration on locally compact noncommutative spaces, Metrics and causality on Moyal planes, Self-dual noncommutative \(\phi^4\)-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory, Quantum field theory on noncommutative spaces, The noncommutative geometry of the Landau Hamiltonian: metric aspects, Index theory for locally compact noncommutative geometries, Noncommutative quantum field theory, Asymptotic and exact expansions of heat traces

Cites Work

• Integration on locally compact noncommutative spaces
• Gravity coupled with matter and the foundation of non-commutative geometry
• Characterization of pseudodifferential operator and application
• The spectral action principle
• On the spectral characterization of manifolds
• On the boundedness of pseudo-differential operators
• Index theory for locally compact noncommutative geometries
• Scale invariance in the spectral action
• Particle models and noncommutative geometry