Optimized Perturbation Theory

  • Antal Jakovác
  • András Patkós
Part of the Lecture Notes in Physics book series (LNP, volume 912)


The aim of this chapter is to present methods for improving the convergence properties of the perturbation theory. In particular, the influence of new energy scales appearing when one embeds a field theory into a specific environment might require critical analysis of the formal perturbation series, since infrared (IR) divergences might be generated by the new scale. The chapter begins with a discussion of the origin of IR singularities. It is followed by the presentation of the general optimization strategy and the question of the renormalizability of optimized series. The detailed implementation of the strategy will be illustrated with the example of the one-component ϕ4-theory. In the second half of the chapter, an enlarged perturbative framework will be introduced when a static resummation is not satisfactory, and a momentum-dependent resummation is needed. This is accomplished by the two-particle-irreducible (2PI) approximation, which is understood in our interpretation also as a specific example of resummation.


Perturbation Theory Mass Parameter Renormalization Scheme Perturbation Series Finite Part 
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.


  1. 1.
    P.M. Stevenson, Phys. Rev. D 23, 2916 (1981)CrossRefADSGoogle Scholar
  2. 2.
    D. O’Connor, C.R. Stephens, Int. J. Mod. Phys. A 9, 2805 (1994)zbMATHMathSciNetCrossRefADSGoogle Scholar
  3. 3.
    S. Chiku, T. Hatsuda, Phys. Rev. D 58, 076001 (1998)CrossRefADSGoogle Scholar
  4. 4.
    S. Chiku, Prog. Theor. Phys. 104, 1129 (2000)CrossRefADSGoogle Scholar
  5. 5.
    L.H. Chan, R.W. Haymaker, Phys. Rev. D 7, 402 (1973)CrossRefADSGoogle Scholar
  6. 6.
    T. Herpay, Zs. Szép, Phys. Rev. D 74, 025008 (2006)Google Scholar
  7. 7.
    A. Jakovác, Zs. Szép, Phys. Rev. D 71, 105001 (2005)Google Scholar
  8. 8.
    P. Petreczky, F. Karsch, A. Patkós, Phys. Lett. B 401, 69 (1997)CrossRefADSGoogle Scholar
  9. 9.
    J.-P. Blaizot, N. Wschebor, Phys. Lett. B741, 310 (2014)Google Scholar
  10. 10.
    P. Kovács, Zs. Szép, Phys. Rev. D 75, 025015 (2007)Google Scholar
  11. 11.
    H.v. Hees, J. Knoll, Phys. Rev. D 65, 025010 (2002)Google Scholar
  12. 12.
    H.v. Hees, J. Knoll, Phys. Rev. D 65, 105005 (2002)Google Scholar
  13. 13.
    H.v. Hees and J. Knoll, Phys. Rev. D 66, 025028 (2002)Google Scholar
  14. 14.
    J.P. Blaizot, E. Iancu, U. Reinosa, Phys. Lett. B 568, 160 (2003)zbMATHMathSciNetCrossRefADSGoogle Scholar
  15. 15.
    J.P. Blaizot, E. Iancu, U. Reinosa, Nucl. Phys. A 736, 149 (2004)CrossRefADSGoogle Scholar
  16. 16.
    F. Cooper, B. Mihaila, J.F. Dawson, Phys. Rev. D 70, 105008 (2004)CrossRefADSGoogle Scholar
  17. 17.
    E. Calzetta, B.L. Hu, Phys. Rev. D 35, 495 (1987)MathSciNetCrossRefADSGoogle Scholar
  18. 18.
    A. Arrizabalaga, J. Smit, Phys. Rev. D 66, 065014 (2002)CrossRefADSGoogle Scholar
  19. 19.
    J. Berges, S. Borsányi, U. Reinosa, J. Serreau, Ann. Phys. 320, 344 (2005)zbMATHCrossRefADSGoogle Scholar
  20. 20.
    A. Patkós, Zs. Szép, Nucl. Phys. A 811, 329 (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Antal Jakovác
    • 1
  • András Patkós
    • 1
  1. 1.Institute of PhysicsRoland Eötvös UniversityBudapestHungary

Personalised recommendations