### 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 Ω_{d} satisfy the conditions of the convergence theorem. For a generic scalar non-commutative quantum field theory on ℝ^{d}, the class Ω_{d} 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 language | English (US) |
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Pages (from-to) | 23-30 |

Number of pages | 8 |

Journal | Journal of High Energy Physics |

Volume | 4 |

Issue number | 5 PART B |

State | Published - Dec 1 2000 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

^{d}, 1. Scalars.

*Journal of High Energy Physics*,

*4*(5 PART B), 23-30.