The spectral action for Moyal planes

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 $\Theta$ 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 $\Theta$.

20 pages, no figure, few improvments

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Cited by in corpus (39)

• Emergent Gravity from Noncommutative Gauge Theory
• Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
• Induced Gauge Theory on a Noncommutative Space
• The spectral distance on the Moyal plane
• Particle Physics from Almost Commutative Spacetimes
• Quantum noncommutative gravity in two dimensions
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Noncommutative geometry, gauge theory and renormalization
• Spectral action beyond the weak-field approximation
• Heat kernel and number theory on NC-torus
• Spectral geometry of the Moyal plane with harmonic propagation
• Heat kernel, effective action and anomalies in noncommutative theories
• Noncommutative QFT and Renormalization
• Cwikel estimates revisited
• Position-dependent noncommutative products: classical construction and field theory
• Spectral action and big desert
• Connes distance by examples: Homothetic spectral metric spaces
• Worldline approach to noncommutative field theory
• Spectral Distances: Results for Moyal Plane and Noncommutative Torus
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Quantum corrections to the noncommutative kink
• Non-compact spectral triples with finite volume
• On space-time noncommutative theories at finite temperature
• Heat Trace Asymptotics on Noncommutative Spaces
• Spectral triplets, statistical mechanics and emergent geometry in non-commutative quantum mechanics
• Space-Time from the spectral point of view
• Spectral Action in Noncommutative Geometry
• Renormalization on noncommutative torus
• Noncommutative Geometry and the Standard Model
• Spectral action on SU_q(2)
• Nilpotent noncommutativity and renormalization
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Induced Chern-Simons action on noncommutative torus
• Diffeomorphisms and orthonormal frames
• A numerical approach to harmonic non-commutative spectral field theory
• Induced Gauge Theory on a Noncommutative Space
• Spectral action in noncommutative geometry: An example
• First numerical approach to a Grosse-Wulkenhaar model
• On space-time noncommutative U(1) model at high temperature