2016/12/22 by Harald Grosse, Grosse, Harald, Akifumi Sako +3 · 2 citations
Mathematics · Physics and Astronomy · #81R12 #81T08 #81T16 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics #Coupling (piping) #Coupling constant #FOS: Physical sciences #Function (biology) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Quantum mechanics #Random Matrices and Applications #Reflection (computer programming) #Scattering #Space (punctuation) #Spectrum (functional analysis) #hep-th #math-ph #math.MP #msc:81R12 #msc:81T08 #msc:81T16
paper · pdf · doi:10.48550/arxiv.1612.07584
published in arXiv (Cornell University) (Cornell University) · 31 pages, 2 figures. LaTeX. Dedicated to the memory of Wolfhart Zimmermann. v2: update of arXiv:1610.00526 permitted to suppress 3 pages
openalex publication_date 2016/12/22 · arxiv created 2017/06/02 · arxiv updated 2017/06/05 · openalex created_date 2022/09/30 · openalex updated_date 2026/08/08
We extend our previous work (on D=2) to give an exact solution of the Φ3D large-N matrix model (or renormalised Kontsevich model) in D=4 and D=6 dimensions. Induction proofs and the difficult combinatorics are unchanged compared with D=2, but the renormalisation - performed according to Zimmermann - is much more involved. As main result we prove that the Schwinger 2-point function resulting from the Φ3D-QFT model on Moyal space satisfies, for real coupling constant, reflection positivity in D=4 and D=6 dimensions. The Källén-Lehmann mass spectrum of the associated Wightman 2-point function describes a scattering part |p|2 ≥ 2μ2 and an isolated fuzzy mass shell around |p|2=μ2.