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Functional Equations

  • Markus Q. Huber
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

This chapter serves as a short introduction to Dyson-Schwinger (DSEs) and functional renormalization group equations (FRGEs). Both systems of equations form complete sets describing the theory exactly. As such they are suited for the investigation of non-perturbative phenomena.

Keywords

Green Function Landau Gauge Functional Renormalization Group Effective Average Action Functional Renormalization Group Equation 
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.

References

  1. 1.
    F.J. Dyson, Phys. Rev. 75, 1736–1755 (1949)MathSciNetCrossRefzbMATHADSGoogle Scholar
  2. 2.
    J.S. Schwinger, Proc. Nat. Acad. Sci. 37, 452–455 (1951)MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    J.S. Schwinger, Proc. Nat. Acad. Sci. 37, 455–459 (1951)MathSciNetCrossRefADSGoogle Scholar
  4. 4.
    R.J. Rivers, Path Integrals Methods in Quantum Field Theory (Cambridge University Press, Cambridge, 1988)Google Scholar
  5. 5.
    R. Alkofer, M.Q. Huber, K. Schwenzer, Comput. Phys. Commun. 180, 965–976 (2009), arXiv:0808.2939 [hep-th]Google Scholar
  6. 6.
    J.A.M. Vermaseren, arXiv:math-ph/0010025Google Scholar
  7. 7.
    S. Wolfram, The Mathematica Book (Cambridge University Press, Cambridge, 1999)Google Scholar
  8. 8.
    S. Diehl, S. Floerchinger, H. Gies, J.M. Pawlowski, C. Wetterich, Annalen Phys. 522, 615−656 (2010), arXiv:0907.2193 [cond-mat.quant-gas]Google Scholar
  9. 9.
    S. Diehl, H. Gies, J.M. Pawlowski, C. Wetterich, Phys. Rev. A 76, 021602 (2007), arXiv:cond-mat/0701198Google Scholar
  10. 10.
    H. Gies, F. Synatschke, A. Wipf, Phys. Rev. D 80, 101701 (2009), arXiv:0906.5492 [hep-th]Google Scholar
  11. 11.
    F. Synatschke, J. Braun, A. Wipf, arXiv:1001.2399 [hep-th]Google Scholar
  12. 12.
    F. Synatschke, H. Gies, A. Wipf, Phys. Rev. D 80, 085007 (2009), arXiv:0907.4229 [hep-th]Google Scholar
  13. 13.
    E. Manrique, M. Reuter, Talk given at international workshop on continuum and lattice approaches to quantum gravity, Brighton, UK, 17–19 Sep 2008, arXiv:0905.4220 [hep-th]Google Scholar
  14. 14.
    M. Reuter, Phys. Rev. D 57, 971–985 (1998), arXiv:hep-th/9605030Google Scholar
  15. 15.
    M. Reuter, F. Saueressig, Phys. Rev. D 65, 065016 (2002), arXiv:hep-th/0110054Google Scholar
  16. 16.
    A. Eichhorn, H. Gies, Phys. Rev. D 81, 104010 (2010), arXiv:1001.5033 [hep-th]Google Scholar
  17. 17.
    A. Eichhorn, H. Gies, M.M. Scherer, Phys. Rev. D 80, 104003 (2009), arXiv:0907.1828 [hep-th]Google Scholar
  18. 18.
    B.-J. Schaefer, J. Wambach, Phys. Part. Nucl. 39, 1025–1032 (2008), arXiv:hep-ph/0611191Google Scholar
  19. 19.
    B.-J. Schaefer, J. Wambach, Phys. Rev. D 75 (2007) 085015, arXiv:hep-ph/0603256Google Scholar
  20. 20.
    J. Braun, H. Gies, J.M. Pawlowski, Phys. Lett. B 684, 262–267 (2010), arXiv:0708.2413 [hep-th]Google Scholar
  21. 21.
    B.-J. Schaefer, M. Wagner, Phys. Rev. D 79, 014018 (2009), arXiv:0808.1491 [hep-ph]Google Scholar
  22. 22.
    J. Braun, L.M. Haas, F. Marhauser, J.M. Pawlowski, Phys. Rev. Lett. 106, 022002 (2011), arXiv:0908.0008 [hep-ph]Google Scholar
  23. 23.
    J. Berges, N. Tetradis, C. Wetterich, Phys. Rept. 363, 223–386 (2002), arXiv:hep-ph/0005122Google Scholar
  24. 24.
    J.M. Pawlowski, Ann. Phys. 322, 2831–2915 (2007), arXiv:hep-th/0512261Google Scholar
  25. 25.
    H. Gies, Presented at ECT* school on renormalization group and effective field theory approaches to many-body systems, Trento, Italy, 27 Feb–10 Mar 2006, arXiv:hep-ph/0611146Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Markus Q. Huber
    • 1
  1. 1.University of GrazGrazAustria

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