Rigorous relativistic equation for quark–antiquark bound states at finite temperature derived from thermal QCD formulated in the coherent-state representation

  • Jun-Chen SuEmail author
Theoretical Physics


A rigorous three-dimensional relativistic equation for quark–antiquark bound states at finite temperature is derived from the thermal QCD generating functional which is formulated in the coherent-state representation. The generating functional is derived newly and given a correct path-integral expression. The perturbative expansion of the generating functional is specifically given by means of the stationary-phase method. Especially, the interaction kernel in the three-dimensional equation is derived by virtue of the equations of motion satisfied by some quark–antiquark Green functions and given a closed form which is expressed in terms of only a few types of Green functions. This kernel is very suitable to use for exploring the deconfinement of quarks. To demonstrate the applicability of the equation derived, the one-gluon exchange kernel is derived and described in detail.


Partition Function Ghost Green Function Perturbative Expansion Position Space 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Gyulassy, Nucl. Phys. A 685, 432 (2001)CrossRefADSGoogle Scholar
  2. 2.
    D. Hardtke, in: Proceedings of XXI International Symposium on Lepton and Photon Interactions at High Energies, p. 329, at Fermilab (2003)Google Scholar
  3. 3.
    R. Stock, J. Phys. G: Nucl. Part. Phys. 30, 633 (2004)CrossRefADSGoogle Scholar
  4. 4.
    Y. Iwasaki, K. Kanaya, S. Kaya, S. Sakai, T. Yoshie, Phys. Rev. D 69, 014507 (2004)CrossRefADSGoogle Scholar
  5. 5.
    M.D. Elia, A. Di Giacomo, E. Meggiolaro, Phys. Rev. D, 114504 (2003)Google Scholar
  6. 6.
    A. Mòcsy, F. Sannino, K. Tuominen, Phys. Rev. Lett. 92, 182302 (2004)CrossRefADSGoogle Scholar
  7. 7.
    Z. Yang, P. Zhuang, Phys. Rev. C 69, 035203 (2004)CrossRefADSGoogle Scholar
  8. 8.
    H. Gies, Phys. Rev. D 63, 025013 (2001)CrossRefADSGoogle Scholar
  9. 9.
    M. Asakawa, U. Heinz, B. Müller, Phys. Rev. Lett. 85, 2072 (2000)CrossRefADSGoogle Scholar
  10. 10.
    H. Li, C.M. Shakin, Phys. Rev. D 66, 074016 (2002)CrossRefADSGoogle Scholar
  11. 11.
    S. Gupta, Phys. Rev. D 64, 034507 (2001)CrossRefADSGoogle Scholar
  12. 12.
    S. Jesgarz, S. Lerma, P.O. Hess, O. Civitarese, M. Reboiro, Phys. Rev. C 67, 055210 (2003)CrossRefADSGoogle Scholar
  13. 13.
    G.F. Burgio, M. Baldo, P.K. Sahu, H.-J. Schulze, Phys. Rev. C 66, 025802 (2002)CrossRefADSGoogle Scholar
  14. 14.
    B. Sheikholeslami-Sabzevari, Phys. Rev. C 65, 054904 (2002)CrossRefADSGoogle Scholar
  15. 15.
    S.S. Wu, J. Phys. G: Nucl. Part. Phys. 16, 1447 (1990); Commun. Theor. Phys. 10, 181 (1988)CrossRefADSGoogle Scholar
  16. 16.
    J.C. Su, J.X. Chen, Phys. Rev. D 69, 076002 (2004)CrossRefADSGoogle Scholar
  17. 17.
    J.C. Su, J. Phys. G: Nucl. Part. Phys. 30, 1309 (2004)CrossRefADSGoogle Scholar
  18. 18.
    A. Casher, D. Lurie, M. Revzen, J. Math. Phys. 9, 1312 (1968)CrossRefGoogle Scholar
  19. 19.
    L.S. Schulman, Techniques and Applications of Path Integration (Wiley-Interscience Publication, New York, 1981)Google Scholar
  20. 20.
    M. Beccaria, B. Allés, F. Farchioni, Phys. Rev. E 55, 3870 (1997)CrossRefADSGoogle Scholar
  21. 21.
    J.W. Negele, H. Orland, Quantum Many-Particle Systems, (Perseus Books Publishing, L.L. C, 1998)Google Scholar
  22. 22.
    M. Le Bellac, Thermal Field Theory (Cambridge University Press, 1996)Google Scholar
  23. 23.
    J.C. Su, Phys. Lett. A 268, 279 (2000)zbMATHMathSciNetCrossRefADSGoogle Scholar
  24. 24.
    S.S. Schweber, J. Math, Phys. 3, 831 (1962)zbMATHMathSciNetGoogle Scholar
  25. 25.
    L.D. Faddeev, A.A. Slavnov, Gauge Fields: Introduction to Quantum Theory (The Benjamin/Cummings Publishing Company, Inc., 1980)Google Scholar
  26. 26.
    C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill Inc., New York, 1980)Google Scholar
  27. 27.
    J.R. Klauder, Phys. Rev. D 19, 2349 (1979)CrossRefADSGoogle Scholar
  28. 28.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963)MathSciNetCrossRefADSGoogle Scholar
  29. 29.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, 1971)Google Scholar
  30. 30.
    D. Lurie, Particles and Fields (Interscience Publishers, New York, 1968)Google Scholar
  31. 31.
    H. Lehmann, Nuovo Cimento 11, 342 (1954)zbMATHMathSciNetGoogle Scholar
  32. 32.
    J.I. Kapusta, Finite-Temperature Field Theory (Cambridge University Press, 1989)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of PhysicsHarbin Institute of TechnologyHarbinP.R. China
  2. 2.Center for Theoretical Physics, School of PhysicsJilin UniversityChangchunP.R. China

Personalised recommendations