Biểu diễn Mellin Hoàn chỉnh Phiên bản Không giao hoán cho Biến thiên Feynman

Abdesselam A. (2004). The Grassmann-Berezin calculus and theorems of the matrix-tree type. Adv. Appl. Math. 33: 51–70, arxiv:math.CO/0306396 Bergère M.C., de Calan C. and Malbouisson A.P.C. (1978). A theorem on asymptotic expansion of Feynman amplitudes. Commun. Math. Phys. 62: 137–158 Bergère M.C. and Lam Y.-M.P. (1974). Asymptotic expansion of Feynman amplitudes Part I The convergent case. Commun. Math. Phys. 39: 1–32 Begère M.C. and Lam Y.-M.P. (1976). Bogolubovâ Parasiuk theorem in the α-parametric representation. J. Math. Phys. 17: 1546–1557 Bergère M.C., Lam Y.-M.P.: preprint, Freie Universität, Berlin, HEP (1979 unpublished) Bergère M.C. and Zuber J.B. (1974). Renormalization of Feynman amplitudes and parametric integral representation. Commun. Math. Phys. 35: 113–140 de Calan C., David F. and Rivasseau V. (1981). Renormalization in the complete Mellin representation of Feynman amplitudes. Commun. Math. Phys. 78: 531–544 de Calan C. and Malbouisson A.P.C. (1980). Complete Mellin representation and asymptotic behaviours of Feynman amplitudes. Ann. Inst. Henri Poincaré 32: 91–107 de Calan C. and Malbouisson A.P.C. (1983). Infrared and ultraviolet dimensional meromorphy of Feynman amplitudes. Commun. Math. Phys. 90: 413–416 Disertori M., Gurau R., Magnen J., Rivasseau V. Vanishing of beta function of non commutative \(\Phi_{4}^{4}\) to all orders. Phys. Lett. B 649, 95–102, arXiv:hep-th/0612251 (2007) Grosse H. and Wulkenhaar R. (2005). Power-counting theorem for non-local matrix models and renormalization, Commun. Math. Phys. 254: 91–127, arXiv:hep-th/0305066 Grosse, H., Wulkenhaar, R.: Renormalization of \(\phi^{4}\) -theory on noncommutative \({\mathbb{R}}^{2}\) in the matrix base, JHEP 12, 019, arXiv:hep-th/0307017 (2003) Grosse, H., Wulkenhaar, R.: Renormalization of \(\phi^{4}\) -theory on noncommutative \({\mathbb{R}}^{4}\) in the matrix base. Commun. Math. Phys. 256, 305–374, arXiv:hep-th/0401128 (2005) Gurau, R., Magnen, J., Rivasseau, V., Vignes-Tourneret, F.: Renormalization of non-commutative \(\phi^4_4\) field theory in x space. Commun. Math. Phys. 267, 515–542, arXiv:hep-th/0512271 (2006) Gurau, R., Rivasseau, V.: Parametric representation of noncommutative field theory. Commun. Math. Phys, 272, 811–835, arxiv:math-ph/0606030 (2007) Gurau, R., Tanasa, A.: Dimensional regularization and renormalization of non-commutative QFT. (submitted to Ann. Henri Poincaré, arXiv:math-ph/0706.1147) Hepp K. (1966). Proof of the Bogoliubov–Parasiuk theorem on renormalization. Commun. Math. Phys. 2: 301–326 Itzykson C. and Zuber J.B. (1980). Quantum Field Theory. McGraw-Hill, New York Langmann, E., Szabo, R.J.: Duality in scalar field theory on noncommutative phase spaces. Phys. Lett. B533, 168–177, arXiv:hep-th0202039 (2002) Linhares, C.A., Malbouisson, A.P.C., Roditi, I.: Asymptotic expansions of Feynman amplitudes in a generic covariant gauge, arxiv:hep-th/0612010 Malbouisson A.P.C. (2000). A convergence theorem for asymptotic expansions of Feynman amplitudes. J. Phys. A: Math. Gen. 33: 3587–3595 Malbouisson A.P.C. (2001). Critical behavior of correlation functions and asymptotic expansions of Feynman amplitudes. In: Janke, W., Pelster, A., Schmidt, H.-J. and Bachmann, M. (eds) Fluctuating Paths and Fields: Festschrift Dedicated to Hagen Kleinert., pp. World Scientific, Singapore Nakanishi N. (1971). Graph Theory and Feynman Integrals. Gordon and Breach, New York Rivasseau, V.: Non-commutative Renormalization. Poincaré Seminar 2007, to appear in Quantum Spaces. Birkhaüser Verlag, arXiv:0705.0705 Rivasseau, V., Tanasa, A.: Parametric representation of “critical” noncommutative QFT models. (submitted to Commun. Math. Phys., arxiv:math-ph/0701034) Rivasseau, V., Vignes-Tourneret, F.: Renormalization of noncommutative field theories, arxiv:hep-th/0702068 Rivasseau, V., Vignes-Tourneret, F., Wulkenhaar, R.: Renormalization of noncommutative \(\phi^4\) -theory by multi-scale analysis. Commun. Math. Phys. 262, 565–594, arXiv: hep-th/0501036 (2006) Vignes-Tourneret, F.: Renormalization of the orientable non-commutative Gross–Neveu model. Ann. H. Poincaré 8, 427–474, arXiv:math-ph/0606069 (2007)