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

Iouri Chepelev, Radu Roiban

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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
Volume4
Issue number5 PART B
StatePublished - Dec 1 2000

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scalars
theorems
diagrams
analogs
subtraction
leaves
ribbons
supersymmetry

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

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Renormalization of quantum field theories on non-commutative ℝd, 1. Scalars. / Chepelev, Iouri; Roiban, Radu.

In: Journal of High Energy Physics, Vol. 4, No. 5 PART B, 01.12.2000, p. 23-30.

Research output: Contribution to journalArticle

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