Zeitschrift für Physik A Hadrons and Nuclei

, Volume 344, Issue 1, pp 99–115 | Cite as

Superconducting quark matter in SU (2) colour group

  • L. A. Kondratyuk
  • M. I. Krivoruchenko
Hadron Physics


The effects of superconductivity of the quark matter in SU(2) colour group are studied. We analyze the QCD-inspired model of interaction of the quarks with the four quark contact interaction which represents relativistic extension of the BCS model. We construct, using the Gor'kov's propagator approach to description of the superconductivity, explicit expressions for the quark propagator, for the anomalous Green's functions, discuss their transformation properties, transformation properties of the order parameters, and find dispersion laws for quasiparticle modes in the one flavour quark matter. There exist two types of solutions of the superconductivity equations corresponding to condensation of the quark Cooper pairs in the triplet spin state. We show that the gap function depends on directions of the quasiparticle momentum and in the massless limit the energy gap vanishes for some directions of the momentum. We estimate the order parameters and critical temperaturs of the phase transition from the normal to the superconducting state, and give expressions for the fermion number density and spin density in the two states of the quark matter. We discuss also analogy between the superconducting quark matter and the nuclear matter in the case of SU(2) colour group. Two quarks in colourless state in SU(2) colour group carry fermion number and should therefore be identified with baryons, so the Cooper pairs in the quark matter can be considered as a kind of baryons present in the quark matter. The superconducting quark matter can be considered as a mixture of quarks and baryons. Such a type of the baryonic matter is shown to obey saturation condition — the well known property of nuclear matter in the real world. The possibility of extension of the model considered to the SU(3) colour group is discussed.


21.90.+f 21.65.+f 12.38.Mb 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Polyakov, A.M.: Phys. Lett. B72, 477 (1978); Susskind, L.: Phys. Rev. D20, 2610 (1979); Olive, K.A.: Nucl. Phys. B190, 483 (1981); Crawford, M., Schramm, D.N.: Nature298, 538 (1982); Schramm, D.N., Olive, K.A.: Nucl. Phys. A418, 289 (1984)Google Scholar
  2. 2.
    Cassing, W., Metag, V., Mosel, U., Niita, K.: Phys. Rep.188, 363 (1990)Google Scholar
  3. 3.
    Ivanenko, D., Kurdgelaidze, D.F.: Lett. Nuovo Cimento2, 13 (1969); Itoh, N.: Progr. Theor. Phys.44, 291 (1970); Chaplin, G., Nauenberg, M.: Nature264, 235, 272 (1976); Kapusta, J.I., Olive, K.A.: Phys. Rev. Lett.64, 13 (1990)Google Scholar
  4. 4.
    Witten, E.: Phys. Rev. D30, 272 (1984); Alcock, C., Farhi, E., Olinto, A.: Astrophys. J.310, 261 (1986); Haensel, P., Zdunik, J.L., Shaeffer, R.: Astron. Ap.160, 121 (1986); Krivoruchenko, M.I.: Pis'ma Zh. Eksp. Teor. Fiz.46, 6 (1987); Alpar, M.A.: Phys. Rev. Lett.58, 2152 (1987); Olinto, A.: Phys. Lett. B192, 71 (1987); Kondratyuk, L.A., Krivoruchenko, M.I., Martemyanov, B.V.: Pis'ma Astron. Zh.16, 954 (1990); Benvenuto, O.G., Horvath, J.E., Vucetich, H.: Phys. Rev. Lett.64, 713 (1990)Google Scholar
  5. 5.
    De Rùjula, Glashow, S.: Nature312, 734 (1984); Farhi, E., Jaffe, R.L.: Phys. Rev. D30, 3279 (1984); Madsen, J.: Phys. Rev. Lett.61, 2909 (1989); Michel, F.C.: Phys. Rev. Lett.60, 677 (1988); Krivoruchenko, M.I., Martemyanov, B.V.: Astrophys. J.378, 628 (1991)Google Scholar
  6. 6.
    Collins, J.C., Perry, M.J.: Phys. Rev. Lett.34, 1353 (1975); Baym, G., Chin, S.: Phys. Rev. Lett. B62, 241 (1976); Kapusta, J.I.: Nucl. Phys. B148, 461 (1979)Google Scholar
  7. 7.
    Cooper, L.N.: Phys. Rev.104, 1189 (1956)Google Scholar
  8. 8.
    Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev.108, 1175 (1957)Google Scholar
  9. 9.
    Bogoliubov, N.N.: Sov. Phys. — JETP7, 41, 51 (1958)Google Scholar
  10. 10.
    Gor'kov, L.P.: Sov. Phys. — JETP7, 505 (1958)Google Scholar
  11. 11.
    Eliasberg, G.M.: Zh. Eksp. Teor. Fiz.38, 966 (1960)Google Scholar
  12. 12.
    Nambu, N.: Phys. Rev.117, 648 (1960)Google Scholar
  13. 13.
    Abrikosov, A.A., Gor'kov, L.P., Dzyaloshinski, I.E.: Methods of quantum field theory in statistical physics. Moscow: Nauka 1961; Lifshits, E.M., Pitaevsky, L.P.: Statistical physics. Part II. Course of theoretical physics, Vol. IX, 2nd ed. Moscow: Nauka 1989; Problems of high temperature conductivity. Ginzburg, V.L., Kirzhnitz, D.A. (eds.). Moscow: Nauka 1977Google Scholar
  14. 14.
    Migdal, A.B.: Zh. Eksp. Teor. Fiz.37, 249 (1959)Google Scholar
  15. 15.
    Ginzburg, V.L., Kirzhnitz, D.A.: Zh. Eksp. Teor. Fiz.47, 2006 (1964)Google Scholar
  16. 16.
    Baym, G., Pethick, C., Pines, D., Ruderman, M.: Nature224, 872 (1969)Google Scholar
  17. 17.
    Pines, D., Alpar, M.A.: Nature316, 27 (1985)Google Scholar
  18. 18.
    Shapiro, S.L., Teukolsky, S.A.: Black holes, white dwarfs, and neutron stars — The physics of compact objects. New York: Wiley 1979Google Scholar
  19. 19.
    Losinskaya, T.A.: Supernova stars and star wind. Interaction with gas of galaxy. Moscow: Nauka 1986Google Scholar
  20. 20.
    Barrois, B.C.: Nucl. Phys. B129, 390 (1977)Google Scholar
  21. 21.
    Bailin, D., Love, A.: J. Phys. A12, L283 (1979)Google Scholar
  22. 22.
    Kondratyuk, L.A., Giannini, M.M., Krivoruchenko, M.I.: Phys. Lett. B269, 139 (1991)Google Scholar
  23. 23.
    Bjorken, J.D., Drell, S.D.: Relativistic quantum mechanics. New York: McGraw-Hill 1964; Relativistic quantum fields. New York: McGraw-Hill 1965Google Scholar
  24. 24.
    Migdal, A.B.: Sov. Phys. — JETP5, 333 (1957)Google Scholar
  25. 25.
    Brown, G.E., Rho, M.: Phys. Lett. B82, 177 (1979); Brown, G.E., Rho, M., Vento, V.: Phys. Lett. B84, 383 (1979); Jaffe, R.L.: Phys. Rev. D21, 3215 (1980); Brown, G.E., Jackson, A.D., Rho, M., Vento, V.: Phys. Lett. B140, 285 (1984); Musakhanov, M.M.: Pis'ma Zh. Eksp. Teor. Fiz.41, 162 (1985)Google Scholar
  26. 26.
    Kobzarev, I.Yu., Martemyanov, B.V., Schepkin, M.G.: Yad. Fiz.29, 1620 (1979); Kondratyuk, L.A., Krivoruchenko, M.I., Schepkin, M.G.: Yad. Fiz.43, 1396 (1986); Pis'ma Zh. Eksp. Teor. Fiz.43, 10 (1986); Yad. Fiz.45, 514 (1987); Nucl. Phys. A473, 746 (1987)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • L. A. Kondratyuk
    • 1
  • M. I. Krivoruchenko
    • 2
    • 3
  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.Dipartimento di FisicaUniversità di GenovaItaly
  3. 3.Sezione di GenovaIstituto Nazionale di Fisica NucleareGenovaItaly

Personalised recommendations