Moyal planes are spectral triples
From MaRDI portal
Publication:701719
zbMath1084.58008arXivhep-th/0307241MaRDI QIDQ701719
Joseph C. Várilly, Victor Gayral, Thomas Schücker, José M. Gracia-Bondía, Bruno Iochum
Publication date: 16 December 2004
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/hep-th/0307241
Noncommutative differential geometry (46L87) Applications of selfadjoint operator algebras to physics (46L60) Noncommutative geometry in quantum theory (81R60) Noncommutative global analysis, noncommutative residues (58J42)
Related Items
The noncommutative geometry of graph \(C^*\)-algebras. I: The index theorem ⋮ Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori ⋮ Dixmier traces and non-commutative analysis ⋮ The quantum Gromov-Hausdorff propinquity ⋮ Quantum Euclidean spaces with noncommutative derivatives ⋮ Isospectral deformations of Eguchi-Hanson spaces as nonunital spectral triples ⋮ How Prof. Zeidler supported our research on exact solution of quantum field theory toy models ⋮ Weyl correspondence for a charged particle in the field of a magnetic monopole ⋮ Nonunital spectral triples and metric completeness in unbounded \(KK\)-theory ⋮ On Hansen's version of spectral theory and the Moyal product ⋮ Twisted reality condition for Dirac operators ⋮ Noncommutative geometry of the Moyal plane: translation isometries, Connes' distance on coherent states, Pythagoras equality ⋮ Position-dependent noncommutative products: classical construction and field theory ⋮ Index theory and adiabatic limit in QFT ⋮ Star product realizations of \(\kappa \)-Minkowski space ⋮ Deformation Quantization for Actions of Kählerian Lie Groups ⋮ Constructive renormalization of the 2-dimensional Grosse-Wulkenhaar model ⋮ A modular spectral triple for \(\kappa\)-Minkowski space ⋮ Dixmier traces for discrete pseudo-differential operators ⋮ Spaces of type \(S\) and deformation quantization ⋮ A \(C^*\)-algebraic approach to the principal symbol. II ⋮ Spectral shift for relative Schatten class perturbations ⋮ Characterization of the Moyal multiplier algebras for the generalized spaces of type \(S\) ⋮ Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering ⋮ Nonlinear partial differential equations on noncommutative Euclidean spaces ⋮ Strict deformation quantization of locally convex algebras and modules ⋮ Sigma-model solitons on noncommutative spaces ⋮ 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory ⋮ Compact \(\kappa \)-deformation and spectral triples ⋮ Deformations of quantum field theories on spacetimes with Killing vector fields ⋮ Integration on locally compact noncommutative spaces ⋮ From Monge to Higgs: a survey of distance computations in noncommutative geometry ⋮ Quantum Metric Spaces and the Gromov-Hausdorff Propinquity ⋮ Metrics and causality on Moyal planes ⋮ Dixmier measurability in Marcinkiewicz spaces and applications ⋮ Revisiting Connes’ finite spectral distance on noncommutative spaces: Moyal plane and fuzzy sphere ⋮ Retarded functions in noncommutative theories ⋮ Heat trace and spectral action on the standard Podleś sphere ⋮ Projective Dirac operators, twisted \(K\)-theory, and local index formula ⋮ Spectral geometry with a cut-off: topological and metric aspects ⋮ Modules over the noncommutative torus and elliptic curves ⋮ Advances in Dixmier traces and applications ⋮ Inclusion theorems for the Moyal multiplier algebras of generalized Gelfand-Shilov spaces ⋮ Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces ⋮ Connes integration formula for the noncommutative plane ⋮ Self-dual noncommutative \(\phi^4\)-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory ⋮ Field theory with coordinate dependent noncommutativity ⋮ Noncommutative manifolds from graph and \(k\)-graph \(C^*\)-algebras ⋮ Spectral action beyond the weak-field approximation ⋮ Quantum differentiability on noncommutative Euclidean spaces ⋮ Noncommutative differential calculus for Moyal subalgebras ⋮ Quantum field theory on noncommutative spaces ⋮ Spectral action and big desert ⋮ Dixmier traces on noncompact isospectral deformations ⋮ The noncommutative geometry of the Landau Hamiltonian: metric aspects ⋮ Renormalisation of \(\phi^4\)-theory on noncommutative \(\mathbb R^{4}\) in the matrix base ⋮ The spectral distance in the Moyal plane ⋮ Conjugate variables in quantum field theory and natural symplectic structures ⋮ K\"ahler geometry on complex projective spaces via reduction and unfolding ⋮ C ∗-completions and the DFR-algebra ⋮ The Dixmier trace and asymptotics of zeta functions ⋮ Dixmier traces and extrapolation description of noncommutative Lorentz spaces ⋮ Wave Equations with Non-commutative Space and Time ⋮ Index theory for locally compact noncommutative geometries ⋮ Spaces of type \(S\) as topological algebras under twisted convolution and star product ⋮ The Moyal sphere ⋮ Spectral triples with multitwisted real structure ⋮ Field theories on deformed spaces ⋮ The Dixmier Trace and the Noncommutative Residue for Multipliers on Compact Manifolds ⋮ Moyal multiplier algebras of the test function spaces of type S ⋮ Star products on symplectic vector spaces: convergence, representations, and extensions ⋮ Quantum causality constraints on kappa-Minkowski space-time