Parametric representation of "covariant" noncommutative QFT models

Communications in Mathematical Physics

Volumn 279, Issue 2, 2008, Pages 355-379

  Rivasseau, Vincent ^a   Tanasǎ, Adrian ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 40249091275     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0437-1     Document Type: Article

References (18)

1. Douglas M. and Nekrasov N. (2001). Noncommutative field theory. Rev. Mod. Phys. 73: 977-1029
2. Connes A., Douglas M.R. and Schwarz A. (1998). Noncommutative Geometry and Matrix Theory: Compactification on Tori. JHEP 9802: 3-43
3. Seiberg N. and Witten E. (1999). String theory and noncommutative geometry. JHEP 9909: 32-131
4. Susskind, L.: The Quantum Hall Fluid and Non-Commutative Chern Simons Theory. http://arxiv.org/list/htp-th/0101029.2001
5. Polychronakos A.P. (2001). Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory. JHEP 06: 70-95
6. Hellerman S. and Van Raamsdonk M. (2001). Quantum Hall physics equals noncommutative field theory. JHEP 10: 39-51
7. Grosse H. and Wulkenhaar R. (2005). Power-counting theorem for non-local matrix models and renormalization. Commun. Math. Phys. 254: 91-127
8. Grosse H. and Wulkenhaar R. (2005). Renormalizationof φ4-theory on noncommutative ℝ4 in the matrix base. Commun. Math. Phys. 256: 305-374
9. Rivasseau V., Vignes-Tourneret F. and Wulkenhaar R. (2006). Renormalization of noncommutative φ 4 4-theory by multi-scale analysis. Commun. Math. Phys. 262: 565-594
10. Gurǎu R., Magnen J., Rivasseau V. and Vignes-Tourneret F. (2006). Renormalization of Non Commutative Φ4 4 Field Theory in Direct Space. Commun. Math. Phys. 267: 515-542
11. Vignes-Tourneret F. (2007). Renormalization of the orientable non-commutative Gross-Neveu model. Ann. Henri Poincaré 8(3): 427-474
12. Langmann E., Szabo R.J. and Zarembo K. (2004). Exact solution of quantum field theory on noncommutative phase spaces. JHEP 0401: 17-87
13. Abdelmalek A. (2004). Grasmann-Berezin Calculus and Theorems of the Matrix-Tree Type. Adv. in Appl. Math. 33: 51-70
14. Gurǎu R. and Rivasseau V. (2007). Parametric representation of noncommutative field theory. Commun. Math. Phys. 272(3): 811-835
15. Itzkinson C. and Zuber J.-B. (1980). Quantum Field Theory. McGraw-Hill, New York
16. Rivasseau V. (1991). From perturbative to Constructive Field Theory. Princeton University Press, Princeton, NJ
17. Gurǎu R., Rivasseau V. and Vignes-Tourneret F. (2006). Propagators for Noncommutative Field Theories. Ann. Henri Poincaré 7(7-8): 1601-1628
18. Filk T. (1996). Divergencies in a field theory on quantum space. Phys. Lett. B 376: 53-58