Moyal Planes are Spectral Triples

2003/07/31 by V. Gayral, J. M. Gracia-Bondía, J.M. Gracia-Bond�a +5 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Axiom #Commutative property #Monomial #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum differential calculus #Spectral triple #hep-th #math.OA

paper · pdf · doi:10.1007/s00220-004-1057-z

published as Commun.Math.Phys.246:569-623,2004 · Latex, 54 pages. Version 3 with Moyal-Wick section updated

arxiv created 2003/10/07 · openalex publication_date 2004/04/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/16 · openalex updated_date 2026/08/05

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 \R^2N 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.

Cited by

• Twisted convolution and Moyal star product of generalized functions
• Field Theory with Coordinate Dependent Noncommutativity
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Noncommutative induced gauge theories on Moyal spaces
• Exploring the Causal Structures of Almost Commutative Geometries
• Spectral geometry of κ-Minkowski space
• Fourier multipliers and their applications to PDE on the quantum Euclidean space