The ${\Phi }_4^3$ and ${\Phi }_6^3$ matricial QFT models have reflection positive two-point function

Abstract

We extend our previous work (on $D=2$) to give an exact solution of the ${\Phi }_D^3$ large-$\mathcal{N}$ 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 ${\Phi }_D^3$-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 $|p{|}^2\ge 2{\mu }^2$ and an isolated fuzzy mass shell around $|p{|}^2={\mu }^2$.

31 pages, 2 figures. LaTeX. Dedicated to the memory of Wolfhart Zimmermann. v2: update of arXiv:1610.00526 permitted to suppress 3 pages

Cited by in corpus (1)

• Exact solution of matricial ${\Phi }_2^3$ quantum field theory