Advertisement

Exploiting the 1, 440-fold symmetry of the master two-loop diagram

  • D. J. Broadhurst
Article

Abstract

The 1, 440-element symmetry group of the generic two-loop diagram of massless scalar field theory in 4-2ω dimensions is computed, using tetrahedral symmetry and star-triangle duality. Constructing all quadratic and quartic polynomial invariants, we expand the diagram throughO(ω5), where one first encounters a coefficient that does not appear to be expressible in terms of the Riemann zeta function, thereby strengthening previous suspicions that genuinely new calculational comoplexity arises at the level of 6-loop renormalization.

Keywords

Field Theory Elementary Particle Quantum Field Theory Symmetry Group Zeta Function 
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.
    K.G. Chetyrkin, F.V. Tkachov: Nucl. Phys.192, 159 (1981)Google Scholar
  2. 2.
    K.G. Chetyrikin, S.G. Gorishny, S.A. Larin, F.V. Tkachov: Phys. Lett.132B, 351 (1983); D.I. Kazakov: Phys. Lett.133B, 406 (1983)Google Scholar
  3. 3.
    D.J. Broadhurst: Massless scalar Feynman diagrams: five loops and beyond. Open University preprint OUT-4102-18 (1985)Google Scholar
  4. 4.
    D.I. Kazakov: TMΦ58, 343 (1984) (in Russian); Dubna lecture notes, E2-84-410 (June 1984)Google Scholar
  5. 5.
    D.J. Broadhurst: Phys. Lett.164B, 356 (1985)Google Scholar
  6. 6.
    G.'t Hooft: private communicationGoogle Scholar
  7. 7.
    S.G. Gorishny, A.P. Isaev: TMΦ62, 345 (1985) (in Russian)Google Scholar
  8. 8.
    K.G. Chetyrkin, A.L. Kataev, F.V. Tkachov: Nucl. Phys.B174, 345 (1980)Google Scholar
  9. 9.
    A.C. Hearn: Reduce user's manual. Rand publication CP78, 1984Google Scholar
  10. 10.
    F.V. Tkachov: TMΦ56, 350 (1983) (in Russian)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • D. J. Broadhurst
    • 1
  1. 1.Department of PhysicsOpen UniversityMilton KeynesUK

Personalised recommendations