User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Renormalization of the commutative scalar theory with harmonic term to all orders

Primary tabs

Marcillaud de Goursac, Axel [UCL]

The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders using multiscale analysis in the momentum space. Then, we consider and compute its one-loop beta function, as well as the one on the degenerate Moyal space.We can finally compare both to the vanishing beta function of the theory with harmonic term on the Moyal space.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2013
Language Anglais
Journal information "Annales Henri Poincare" - Vol. 14, p. 2025-2043 (2013)
Peer reviewed yes
Publisher Birkhaeuser Verlag AG ((Switzerland) Basel)
issn 1424-0637
e-issn 1424-0661
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Quantum Field Theory ; Renormalization ; Multiscale analysis ; Beta function
Links
  1. Douglas Michael, Nekrasov Nikita, Noncommutative field theory, 10.1103/revmodphys.73.977
  2. Wulkenhaar Raimar, Field theories on deformed spaces, 10.1016/j.geomphys.2005.04.019
  3. Connes A.: Noncommutative Geometry. Academic Press, San Diego (1994)
  4. Dubois‐Violette Michel, Kerner Richard, Madore John, Noncommutative differential geometry of matrix algebras, 10.1063/1.528916
  5. Connes Alain, Lott John, Particle models and noncommutative geometry, 10.1016/0920-5632(91)90120-4
  6. de Goursac Axel, Masson Thierry, Wallet Jean-Christophe, Noncommutative ε-graded connections, 10.4171/jncg/94
  7. Cagnache Eric, Masson Thierry, Wallet Jean-Christophe, Noncommutative Yang–Mills–Higgs actions from derivation-based differential calculus, 10.4171/jncg/69
  8. Grosse Harald, Wulkenhaar Raimar, Renormalisation of ?4-Theory on Noncommutative ?4 in the Matrix Base, 10.1007/s00220-004-1285-2
  9. Minwalla Shiraz, Raamsdonk Mark Van, Seiberg Nathan, Noncommutative perturbative dynamics, 10.1088/1126-6708/2000/02/020
  10. Rivasseau Vincent, Vignes-Tourneret Fabien, Wulkenhaar Raimar, Renormalisation of Noncommutative ϕ4-Theory by Multi-Scale Analysis, 10.1007/s00220-005-1440-4
  11. Gurau Razvan, Magnen Jacques, Rivasseau Vincent, Vignes-Tourneret Fabien, Renormalization of Non-Commutative $$\Phi^4_4$$ Field Theory in x Space, 10.1007/s00220-006-0055-8
  12. Gurău Razvan, Tanasă Adrian, Dimensional Regularization and Renormalization of Non-Commutative Quantum Field Theory, 10.1007/s00023-008-0363-y
  13. Tanasă Adrian, Vignes-Tourneret Fabien, Hopf algebra of non-commutative field theory, 10.4171/jncg/17
  14. Wulkenhaar R., Grosse H., The $\beta$ -function in duality-covariant non-commutative $\phi^4$ -theory, 10.1140/epjc/s2004-01853-x
  15. Disertori Margherita, Gurau Razvan, Magnen Jacques, Rivasseau Vincent, Vanishing of beta function of non-commutative Φ44 theory to all orders, 10.1016/j.physletb.2007.04.007
  16. Grosse, H., Wulkenhaar, R.: Self-dual noncommutative phi4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory. arXiv:1205.0465 [math-ph]
  17. Langmann Edwin, Szabo Richard J., Duality in scalar field theory on noncommutative phase spaces, 10.1016/s0370-2693(02)01650-7
  18. de Goursac A.: On the origin of the harmonic term in noncommutative quantum field theory. SIGMA 6, 048 (2010)
  19. de Goursac A., Tanasa A., Wallet J.-C., Vacuum configurations for renormalizable non-commutative scalar models, 10.1140/epjc/s10052-007-0465-6
  20. Hounkonnou M N, Ousmane Samary D, Twisted Grosse–Wulkenhaar φ⋆4model: dynamical noncommutativity and Noether currents, 10.1088/1751-8113/43/15/155202
  21. Geloun Joseph Ben, Hounkonnou Mahouton Norbert, Energy–momentum tensors in renormalizable noncommutative scalar field theory, 10.1016/j.physletb.2007.08.029
  22. de Goursac Axel, Wallet Jean-Christophe, Symmetries of noncommutative scalar field theory, 10.1088/1751-8113/44/5/055401
  23. Langmann E, Szabo R.J, Zarembo K, Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces, 10.1088/1126-6708/2004/01/017
  24. Vignes-Tourneret Fabien, Renormalization of the Orientable Non-commutative Gross–Neveu Model, 10.1007/s00023-006-0312-6
  25. Gurau R., Magnen J., Rivasseau V., Tanasa A., A Translation-Invariant Renormalizable Non-Commutative Scalar Model, 10.1007/s00220-008-0658-3
  26. Geloun Joseph Ben, Tanasa Adrian, One-Loop β Functions of a Translation-Invariant Renormalizable Noncommutative Scalar Model, 10.1007/s11005-008-0270-7
  27. Magnen J., Rivasseau V., Tanasa A., Commutative limit of a renormalizable noncommutative model, 10.1209/0295-5075/86/11001
  28. Blaschke Daniel N, Gieres François, Kronberger Erwin, Schweda Manfred, Wohlgenannt Michael, Translation-invariant models for non-commutative gauge fields, 10.1088/1751-8113/41/25/252002
  29. Blaschke Daniel N., Rofner Arnold, Schweda Manfred, Sedmik René I. P., One-loop calculations for a translation invariant non-commutative gauge model, 10.1140/epjc/s10052-009-1031-1
  30. Pinzul A, UV/IR mixing as a twisted Poincaré anomaly, 10.1088/1751-8113/45/7/075401
  31. Liang Mai-Lin, Jiang Yue, Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane, 10.1016/j.physleta.2010.10.035
  32. de Goursac A., Wallet J.-C., Wulkenhaar R., Noncommutative induced gauge theory, 10.1140/epjc/s10052-007-0335-2
  33. Grosse H., Wohlgenannt M., Induced gauge theory on a noncommutative space, 10.1140/epjc/s10052-007-0369-5
  34. de Goursac A., Wallet J.-C., Wulkenhaar R., On the vacuum states for non-commutative gauge theory, 10.1140/epjc/s10052-008-0652-0
  35. Blaschke D. N, Grosse H, Schweda M, Non-commutative U(1) gauge theory on with oscillator term and BRST symmetry, 10.1209/0295-5075/79/61002
  36. Blaschke, D.N., Grosse, H., Kronberger, E., Schweda, M., Wohlgenannt, M.: Loop calculations for the non-commutative U(1) gauge field model with oscillator term. arXiv:0912.3642 [hep-th]
  37. Wulkenhaar, R.: Non-compact spectral triples with finite volume. arXiv: 0907.1351 [hep-th]
  38. Rivasseau V., From Perturbative to Constructive Renormalization : , ISBN:9781400862085, 10.1515/9781400862085
  39. Vignes-Tourneret, F.: Renormalisation of non commutative field theories. arXiv: math-ph/0612014
  40. Zimmermann W., Convergence of Bogoliubov's method of renormalization in momentum space, 10.1007/bf01645676
  41. Bieliavsky Pierre, de Goursac Axel, Tuynman Gijs, Deformation quantization for Heisenberg supergroup, 10.1016/j.jfa.2012.05.002
  42. de Goursac, A.: On the Hopf algebra setting of the flat superspace’s deformation. arXiv:1105.2420 [math.QA]
  43. Gurau Razvan, Rivasseau Vincent, Vignes-Tourneret Fabien, Propagators for Noncommutative Field Theories, 10.1007/s00023-006-0296-2
  44. Grosse Harald, Vignes-Tourneret Fabien, Quantum field theory on the degenerate Moyal space, 10.4171/jncg/66
  45. Grosse, H., Wohlgenannt, M.: Degenerate noncommutativity. arXiv:1201.5982 [hep-th]
Bibliographic reference Marcillaud de Goursac, Axel. Renormalization of the commutative scalar theory with harmonic term to all orders. In: Annales Henri Poincare, Vol. 14, p. 2025-2043 (2013)
Permanent URL http://hdl.handle.net/2078.1/136997