Renormalization of quantum field theories on non-commutative ℝd, 1. Scalars

Iouri Chepelev, Radu Roiban

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


A non-commutative Feynman graph is a ribbon graph and can be drawn on a genus g 2-surface with a boundary. We formulate a general convergence theorem for the non-commutative Feynman graphs in topological terms and prove it for some classes of diagrams in the scalar field theories. We propose a non-commutative analog of Bogoliubov-Parasiuk's recursive subtraction formula and show that the subtracted graphs from a class Ωd satisfy the conditions of the convergence theorem. For a generic scalar non-commutative quantum field theory on ℝd, the class Ωd is smaller than the class of all diagrams in the theory. This leaves open the question of perturbative renormalizability of non-commutative field theories. We comment on how the supersymmetry can improve the situation and suggest that a non-commutative analog of Wess-Zumino model is renormalizable.

Original languageEnglish (US)
Pages (from-to)23-30
Number of pages8
JournalJournal of High Energy Physics
Issue number5 PART B
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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