2014/02/28 by Antoine Géré, Jean-Christophe Wallet · 4 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Bounded function #Dirac operator #Homotopy and Cohomology in Algebraic Topology #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Operator (biology) #Quantum differential calculus #Spectral theory of ordinary differential equations #Spectral triple #Spectrum (functional analysis) #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-6596/634/1/012006
published in Journal of Physics Conference Series 634, 012006 (IOP Publishing) · 31 pages. Improved version to be published. Section 4 modified. Various misprints corrected
arxiv created 2015/06/26 · openalex publication_date 2015/08/03 · arxiv updated 2015/08/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral theory is given in a way applicable to the study of NCFT. As an illustration, this is applied to a gauge-fixed version of the induced gauge theory on the Moyal plane expanded around a symmetric vacuum. The characterization of the spectrum of the kinetic operator is given, showing a behavior somewhat similar to a massless theory. An attempt to characterize the noncommutative geometry related to the gauge fixed action is presented. Using a Dirac operator obtained from the kinetic operator, it is shown that one can construct an even, regular, weakly real spectral triple. This spectral triple does not define a noncommutative metric space for the Connes spectral distance.