Advertisement

Non-Commutative Renormalization

  • Vincent Rivasseau
  • Fabien Vignes-Tourneret
Part of the Progress in Mathematics book series (PM, volume 251)

Summary

We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non-commutative field theory and suggest a related constructive program. This paper is dedicated to J. Bros on his 70th birthday.

Keywords

Matrix Model Star Product Matrix Base Commutative Case Gaussian Wave Packet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. R, Douglas and N. A. Nekrasov: Non commutative Field Theory. arXiv:hep-th0106048.Google Scholar
  2. 2.
    S. Minwalla, M. Van Raamsdonk and N. Seiberg: Non commutative perturbative dynamics. JHEP 0002:020 (2000).ADSCrossRefMATHGoogle Scholar
  3. 3.
    I. Chepelev and R. Roiban: Renormalization of quantum field theories on non-commutative IRd. I: Scalars. JHEP 0005:037 (2000).ADSMathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    I. Chepelev and R. Roiban: Convergence Theorems for non-commutative Feynman graphs and renormalization. JHEP 0103:001 (2001).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    H. Grosse and R. Wulkenhaar: Power Counting Theorems for non-local matrix models and renormalization. arXiv:hep-th/0305066.Google Scholar
  6. 6.
    H. Grosse and R. Wulkenhaar: Renormalization of φ 4 theory on noncommutative IR2 in the matrix base. arXiv:hep-th/0307017.Google Scholar
  7. 7.
    H. Grosse and R. Wulkenhaar. Renormalization of φ 4 theory on noncommutative IR4 in the matrix base. arXiv:hep-th/0401128.Google Scholar
  8. 8.
    E. Langmann and R.J. Szabo: Duality in scalar field theory on noncommutative phase space. Phys Lett. B 553:168 (2002).ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    V. Rivasseau, F. Vignes-Tourneret and R. Wulkenhaar: To appear.Google Scholar
  10. 10.
    R. Koekoek and R. F. Swarttouw: The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. arXiv:math.CA/9602214.Google Scholar
  11. 11.
    J. Polchinski: Renormalization and Effective Lagrangians. Nucl. Phys B 231:269 (1984).ADSCrossRefGoogle Scholar
  12. 12.
    M. Disertori and V. Rivasseau: Continuous Constructive Fermionic Renormalization. Ann. Henri Poincaré 1:1 (2000).ADSMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    V. Rivasseau: From perturbative to constructive renormalization. Princeton University Press, 1991.Google Scholar
  14. 14.
    V. Rivasseau (ed.): Constructive Physics. Proceedings of the International Workshop at Ecole Polytechnique, Palaiseau, July 1994. Lecture Notes in Physics 446, Springer Verlag, 1995.Google Scholar
  15. 15.
    E.T. Akhmedov, P. de Boer and G.W. Semenoff: Non Commutative Gross-Neveu Model at large N. arXiv:hep-th/0103199.Google Scholar
  16. 16.
    C. Kopper, J. Magnen and V. Rivasseau: Mass Generation in the Large N Gross-Neveu Model. Commun. Math. Phys. 169:121 (1995).ADSMathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    M. Disertori and V. Rivasseau: Interacting Fermi liquid in two dimensions at finite temperature, Part I and II. Commun. Math. Phys. 215:251 and 291 (2000).ADSMathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Joel Feldman, H. Knörrer and E. Trubowitz: A two dimensional Fermi Liquid. Commun. Math. Phys. 247:1–319 (2004); and Reviews in Math. Physics 15(9):949–1169 (2003).ADSMathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    M. Disertori, J. Magnen and V. Rivasseau: Interacting Fermi liquid in three dimensions at finite temperature, part I: Convergent Contributions. Ann. Henri Poincaré 2:733–806 (2001).ADSMathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    H. Grosse and R. Wulkenhaar: The β-function in duality-covariant noncommutative φ 4-theory. arXiv:hep-th/ 0402093.Google Scholar

Copyright information

© Birkhäuser Verlag 2007

Authors and Affiliations

  • Vincent Rivasseau
    • 1
  • Fabien Vignes-Tourneret
    • 1
  1. 1.Laboratoire de Physique ThéoriqueUniversité Paris-Sud XIOrsay CedexFrance

Personalised recommendations