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 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 - 2000 |
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics