Skip to main content
SpringerLink
Log in

Renormalisation of Φ4-Theory on Non-Commutative \(\mathbb{R}^{4}\) to All Orders

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We present the main ideas and techniques of the proof that the duality-covariant four-dimensional non-commutative Φ4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the free theory by orthogonal polynomials as well as the renormalisation byflow equations involving power-counting theorems for ribbon graphs drawn on Riemann surfaces

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Seiberg, N. and Witten, E.: String theory and noncommutative geometry, JHEP 9909 (1999) 032 [arXiv:hep-th/9908142].

  • Minwalla, S., Van Raamsdonk, M. and Seiberg, N.: Noncommutative perturbative dynamics, JHEP 0002 (2000), 020 [arXiv:hep-th/9912072].

  • Chepelev, I. and Roiban, R.: Convergence theorem for non-commutative Feynman graphs and renormalization, JHEP 0103 (2001), 001 [arXiv:hep-th/0008090].

  • Grosse, H. and Wulkenhaar, R.: Renormalisation of Φ4-theory on noncommutative \(\mathbb{R}^{4}\) in the matrix base, arXiv:hep-th/0401128, to appear in Commun. Math. Phys.

  • Grosse, H. and Wulkenhaar, R.: Power-counting theorem for non-local matrix models and renormalisation, arXiv:hep-th/0305066, to appear in Commun. Math. Phys.

  • Langmann, E. and Szabo, R. J.: Duality in scalar field theory on noncommutative phase spaces, Phys. Lett. B 533 (2002), 168 [arXiv:hep-th/0202039].

    Google Scholar 

  • K.G. Wilson J.B. Kogut (1974) ArticleTitleThe renormalization group and the epsilon expansion Phys. Rept. 12 75 Occurrence Handle1025.68695

    MATH  Google Scholar 

  • J Polchinski (1984) ArticleTitleRenormalization and effective lagrangians Nucl. Phys. B 231 269

    Google Scholar 

  • Grosse, H. and Wulkenhaar, R.: The β-function in duality-covariant noncommutative φ4 -theory, Eur. Phys. J. C 35 (2004), 277 [arXiv:hep-th/0402093].

    Google Scholar 

  • V. Rivasseau (1991) From Perturbative to Constructive Renormalization Princeton University Press Princeton

    Google Scholar 

  • Langmann, E., Szabo, R. J. and Zarembo, K.: Exact solution of quantum field theory on noncommutative phase spaces, JHEP 0401 (2004), 017 [arXiv:hep-th/0308043].

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria

    Harald Grosse

  2. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraβe 22-26, D-04103, Leipzig, Germany

    Raimar Wulkenhaar

Authors
  1. Harald Grosse
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raimar Wulkenhaar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Harald Grosse.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grosse, H., Wulkenhaar, R. Renormalisation of Φ4-Theory on Non-Commutative \(\mathbb{R}^{4}\) to All Orders. Lett Math Phys 71, 13–26 (2005). https://doi.org/10.1007/s11005-004-5116-3

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-004-5116-3

Keywords

Search

Navigation