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Few-Body Systems

, Volume 48, Issue 1, pp 41–52 | Cite as

Chiral Symmetry Breaking and Confinement in Minkowski Space QED2+1

  • Vladimir ŠauliEmail author
  • Zoltan Batiz
Article

Abstract

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e.g. with the standard Euclidean calculation.

Keywords

Chiral Symmetry Minkowski Space Mass Function Chiral Symmetry Breaking Landau Gauge 
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.

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References

  1. 1.
    Pisarski R.D.: Critical behavior in (2 + 1)-dimensional QED. Phys. Rev. D 29, 2423 (1984)CrossRefADSGoogle Scholar
  2. 2.
    Appelquist T.W., Bowick M., Karabali D., Wijewarhana L.C.R.: Spontaneous chiral-symmetry breaking in three-dimensional QED. Phys. Rev. D 33, 3704 (1986)CrossRefADSGoogle Scholar
  3. 3.
    Appelquist T., Nash D., Wijewardhana L.C.R.: Critical behavior in (2 + 1)-dimensional QED. Phys. Rev. Lett. 60, 2575 (1988)CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Bashir A., Raya A.: Truncated Schwinger–Dyson equations and gauge covariance in QED3. Few Body Syst. 41, 185 (2007)CrossRefADSGoogle Scholar
  5. 5.
    Bashir A., Raya A., Cloet I.C., Roberts C.D.: Regarding confinement and dynamical chiral symmetry breaking in QED3. Phys. Rev. C 78, 055201 (2008)CrossRefADSGoogle Scholar
  6. 6.
    Dagotto E., Kogut J.B., Kocic A.: Computer simulation of chiral-symmetry breaking in (2 + 1)-dimensional QED with N flavors. Phys. Rev. Lett. 62, 1083 (1989)CrossRefADSGoogle Scholar
  7. 7.
    Burden C.J., Praschifka J., Roberts C.D.: Photon polarization tensor in three-dimensional quantum electrodynamics. Phys. Rev. D 46, 2695 (1992)CrossRefADSGoogle Scholar
  8. 8.
    Gusynin V.P., Hams A.H., Reenders M.: (2 + 1)-Dimensional QED with dynamically massive fermions in the vacuum polarization. Phys. Rev. D 53, 2227 (1996)CrossRefADSGoogle Scholar
  9. 9.
    Maris P.: Confinement and complex singularities in QED3. Phys. Rev. D 52, 6087 (1995)CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Fischer C.S., Alkofer R., Dahm T., Maris P.: Dynamical chiral symmetry breaking in unquenched QED 3. Phys. Rev. D 70, 073007 (2004)CrossRefADSGoogle Scholar
  11. 11.
    He M., Feng H.T., Sun W.M., Zong H.S.: Phase structure of QED(3) at finite chemical potential and temperature. Mod. Phys. Lett. A 22, 449 (2007)CrossRefADSGoogle Scholar
  12. 12.
    Franz M., Tesanovic Z., Vafek O.: QED3 theory of pairing pseudogap in cuprates: from d-wave superconductor to antiferromagnet via “algebraic” fermi liquid. Phys. Rev. B 66, 054535 (2002)CrossRefADSGoogle Scholar
  13. 13.
    Herbut I.F.: QED3 theory of underdoped high temperature superconductors. Phys. Rev. B 66, 094504 (2002)CrossRefADSGoogle Scholar
  14. 14.
    Ashot M., Tesanovic Z.: Model of phase fluctuations in a lattice d-wave superconductor: application to the cooperpair charge-density wave in underdoped cuprates. Phys. Rev. B 71, 214511 (2005)CrossRefGoogle Scholar
  15. 15.
    Thomas I.O., Hands S.: Chiral symmetry restoration in anisotropic QED(3). Phys. Rev. B 75, 134516 (2007)CrossRefADSGoogle Scholar
  16. 16.
    Nogueira F.S., Kleinert H.: Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids. Phys. Rev. Lett. 95, 176406 (2005)CrossRefADSGoogle Scholar
  17. 17.
    Novoselov K.S. et al.: Two-dimensional gas of massless dirac fermions in graphene. Nature 438, 197 (2005)CrossRefADSGoogle Scholar
  18. 18.
    Gusynin V.P., Sharapov S.G., Carbotte J.P.: AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics. Int. J. Mod. Phys. B 21, 4611 (2007)CrossRefADSGoogle Scholar
  19. 19.
    Wick G.C.: Properties of Bethe-Salpeter wave functions. Phys. Rev. 96, 1124 (1954)zbMATHCrossRefMathSciNetADSGoogle Scholar
  20. 20.
    Roberts C.D., Williams A.G.: Dyson–Schwinger equations and their application to hadronic physics. Prog. Part. Nucl. Phys. 33, 447 (1994)CrossRefADSGoogle Scholar
  21. 21.
    Roberts C.D., Schmidt S.M.: Dyson–Schwinger equations: density, temperature and continuum strong QCD. Prog. Part. Nucl. Phys. 45, 1 (2000)CrossRefADSGoogle Scholar
  22. 22.
    Sauli, V., Batiz, Z.: General method of solution of Schwinger–Dyson equations in minkowski space, PoS QCD-TNT09:040 (2009). arXiv:0911.0275v1Google Scholar
  23. 23.
    Streater R.F., Wightman A.S.: PCT, Spin and statistics, 3rd edn. Addison-Wesley, Reading (1980)Google Scholar
  24. 24.
    Glimm J., Jaffe A.: Quantum Physics. A functional point of view. Springer, New York (1981)zbMATHGoogle Scholar
  25. 25.
    Sauli V., Batiz Z.: Quark Schwinger-Dyson equation in temporal Euclidean space. J. Phys. G 36, 035002 (2009)CrossRefADSGoogle Scholar
  26. 26.
    Cornwall J.M.: Confinement and chiral-symmetry breakdown: estimates of Fπ and of effective quark masses. Phys. Rev. D 22, 1452 (1980)CrossRefADSGoogle Scholar
  27. 27.
    Gogoghia V.S., Magradze B.A.: Infrared finite quark propagator and chiral symmetry breaking in QCD. Phys. Lett. B 217, 162 (1989)CrossRefADSGoogle Scholar
  28. 28.
    Gribov, V.N.: Possible solution of the problem of quark confinement, unpublished, U. of Lund preprint LU TP 91-7Google Scholar
  29. 29.
    Roberts C.D., Wiliams A.G., Krein G.: On the implications of confinement. Int. J. Mod. Phys. A 5607, 5607 (1992)CrossRefADSGoogle Scholar
  30. 30.
    Alkofer R., Smekal L.: The infrared behavior of QCD Green’s Functions - Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states. Phys. Rep. 353, 281 (2001)zbMATHCrossRefMathSciNetADSGoogle Scholar
  31. 31.
    Alkofer R., Detmold W., Fischer C.S., Maris P.: Analytic properties of the landau gauge gluon and quark propagators. Phys. Rev. D 70, 014014 (2004)CrossRefADSGoogle Scholar
  32. 32.
    Bashir A., Raya A., Sanchez-Madrigal S., Roberts C.D.: Gauge invariance of a critical number of flavours in QED3. Few Body Syst. 46, 229 (2009) arXiv:0905.1337CrossRefADSGoogle Scholar
  33. 33.
    Nickel B.G.: Evaluation of simple feynman graphs. J. Math. Phys. 19, 542 (1978)CrossRefMathSciNetADSGoogle Scholar
  34. 34.
    Davydychev A.I., Osland P., Saks L.: Quark-gluon vertex in arbitrary gauge and dimension. Phys. Rev. D 63, 014022 (2000)CrossRefADSGoogle Scholar
  35. 35.
    Sauli, V.: Infrared behaviour of propagator and quark confinement. arXiv:0902.1195Google Scholar
  36. 36.
    Herbut I.F., Lee D.J.: Theory of spin response in underdoped cuprates as strongly fluctuating d-wave superconductors. Phys. Rev. B 68, 104518 (2003)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.CFTP and Department of PhysicsISTLisbonPortugal
  2. 2.Department of Theoretical PhysicsINP, AVČRŘež near PragueCzech Republic

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