A translation-invariant renormalizable non-commutative scalar model

Communications in Mathematical Physics

Volumn 287, Issue 1, 2009, Pages 275-290

  Gurau, R ^a   Magnen, J ^b   Rivasseau, V ^a   Tanasa, A ^c,d  

^a UNIVERSITÉ PARIS SUD   (France)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c Institutul de Fizica Si Inginerie Nucleara Horia Hulubei   (Romania)

^d MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60449086251     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0658-3     Document Type: Article

References (32)

1. Connes, A.: Géometrie non commutative. Paris: InterEditions, 1990
2. H.S. Snyder 1947 Deformation quantization for actions of the affine group Phys. Rev. 71 38
3. A. Connes M.R. Douglas A. Schwarz 1998 Noncommutative Geometry and Matrix Theory: Compactification on Tori JHEP 9802 3 43
4. N. Seiberg E. Witten 1999 String theory and noncommutative geometry JHEP 9909 32 131
5. Susskind, L.: The Quantum Hall Fluid and Non-Commutative Chern Simons Theory. http://arxiv.org/list/hep-th/0101029, 2001
6. A.P. Polychronakos 2001 Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory JHEP 06 70 95
7. S. Hellerman M. Van Raamsdonk 2001 Quantum Hall physics equals noncommutative field theory JHEP 10 39 51
8. S. Minwalla M. Van Raamsdonk N. Seiberg 2000 Noncommutative perturbative dynamics JHEP 0002 020
9. Bahns, D.: The shuffle Hopf algebra and quasiplanar Wick products, conference proceedings. Non commutative Geometry and Physics, (Orsay, April 2007), http://arXiv.org/abs/0710.2787v1 [math.QA], 2007
10. H. Grosse R. Wulkenhaar 2005 Power-counting theorem for non-local matrix models and renormalization Commun. Math. Phys. 254 91 127
11. 4-theory on noncommutative R4 in the matrix base Commun. Math. Phys. 256 305 374
12. E. Langmann R.J. Szabo 2002 Duality in scalar field theory on noncommutative phase spaces Phys. Lett. B 533 168
13. V. Rivasseau F. Vignes-Tourneret R. Wulkenhaar 2006 Renormalization of noncommutative φ4 -theory by multi-scale analysis Commun. Math. Phys. 262 565 594
14. R. Gurau J. Magnen V. Rivasseau F. Vignes-Tourneret 2006 Renormalization of non-commutative φ4 field theory in x space Commun. Math. Phys. 267 515
15. 4 theory Eur. Phys. J. C 35 277
16. M. Disertori V. Rivasseau 2007 Two and three loops beta function of non-commutative phi(4)4 theory Eur. Phys. J. C 50 661
17. M. Disertori R. Gurau J. Magnen V. Rivasseau 2007 Vanishing of beta function of non-commutative φ4 theory to all orders Phys. Lett. B 649 95
18. R. Gurǎu V. Rivasseau 2007 Parametric representation of noncommutative field theory Commun. Math. Phys. 272 811
19. V. Rivasseau A. Tanasa 2008 Parametric representation of 'covariant' noncommutative QFT models Commun. Math. Phys. 279 2 355 379
20. Gurau, R., Malbouisson, A.P.C., Rivasseau, V., Tanasa, A.: Non-Commutative Complete Mellin Representation for Feynman Amplitudes. http://arXiv.org/abs/0705.3437v1 [math-ph], 2007
21. Gurau, R., Tanasa, A.: Dimensional regularization and renormalization of non-commutative QFT. Submitted to Annales Henri Poincare, http://arXiv.org/abs/ 0706.1147v1 [math-ph], 2007
22. A. Tanasa F. Vignes-Tourneret 2008 Hopf algebra of non-commutative field theory Journ. Noncomm. Geom. 2 125 139
23. F. Vignes-Tourneret 2007 Renormalization of the orientable non-commutative Gross-Neveu model Annales Henri Poincare 8 427
24. Duplantier, B., Rivasseau, V. eds.: Quantum Spaces, Progress in Mathematical Physics 53, Basel-Bosten: Birkhäuser, 2007
25. E. Langmann R.J. Szabo K. Zarembo 2004 Exact solution of quantum field theory on noncommutative phase spaces JHEP 0401 17 87
26. A. de Goursac J.C. Wallet R. Wulkenhaar 2007 Noncommutative induced gauge theory Eur. Phy. J. C 51 977
27. Grosse, H., Wohlgenannt, M.: Induced Gauge Theory on a Noncommutative Space. http://arXiv.org/list/hep-th/0703169, 2007
28. Grosse, H., Wulkenhaar, R.: 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory. http://arXiv.org/abs/0709.0095, V1 [hep-th], 2007
29. A. de Goursac A. Tanasa J.C. Wallet 2008 Vacuum configurations for renormalizable non-commutative scalar models Eur. Phys. J. C 53 459
30. Helling, R.C., You, J.: Macroscopic Screening of Coulomb Potentials From UV/IR-Mixing. http://arXiv.org/abs/0707.1885v.2 [hep-th], 2007
31. T. Filk 1996 Phys. Lett. B 376 53
32. Rivasseau V.: From perturbative to Constructive Field Theory. Princeton University Press, Princeton, NJ (1991)