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Applications to Matter with High Energy Density

  • Werner EbelingEmail author
  • Vladimir E. Fortov
  • Vladimir Filinov
Chapter
Part of the Springer Series in Plasma Science and Technology book series (SSPST)

Abstract

The most fundamental approach to study relativistic quantum systems of many particles is currently a quantum field theory (QFT). In these theories, particles are usually considered as elementary excitations of the corresponding field. This approach automatically takes into account the creation and annihilation of particles, and treats interactions as exchange of virtual particles. The main working tool in QFT is the Feynman diagram technique (Schweber 1963), which represents a series generated in perturbation theory graphically, assuming that the coupling constants are small parameters. Feynman diagrams are useless for strongly coupled systems of particles. One of the most straightforward approaches that can be used to calculate the properties of strongly coupled nonideal systems is lattice QFT. However, calculations on lattices are very costly and require powerful supercomputers. An alternative approach to study relativistic systems is to make use of the path integral model of a system with a variable number of particles described by a Hamiltonian with relativistic kinetic energy operator \(\sqrt{p^2c^2 + m^2c^4}\) and interacting through some effective pair potential. This method has been used to calculate thermodynamic and transport properties of quark–gluon plasmas (Filinov et al. 2012). This requires far fewer computer resources and could be applied to systems with large chemical potentials. Furthermore, an analogous approach has been used in applications to electromagnetic (Filinov et al. 2001) and electron–hole plasmas (Filinov et al. 2007).

References

  1. M. Asakawa, T. Hatsuda, Y. Nakahara, Prog. Part. Nucl. Phys. 46, 459 (2001); Nucl. Phys. A 715, 863 (2003) [Nucl. Phys. Proc. Suppl. 119, 481 (2003)]; M. Asakawa, T. Hatsuda. Phys. Rev. Lett. 92, 12001 (2004)Google Scholar
  2. A. Bazavov et al., Phys. Rev. D 80, 014504 (2009)ADSCrossRefGoogle Scholar
  3. J. Blaizot, E. Iancu, Phys. Rep. 359, 355 (2002)ADSCrossRefGoogle Scholar
  4. M. Bonitz, D. Semkat (eds.), Introduction to Computational Methods for Many Body Systems (Rinton Press, Princeton, 2006)zbMATHGoogle Scholar
  5. S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S.D. Katz, S. Krieg, C. Ratti, K.K. Szabo, JHEP 1011, 77 (2010)ADSCrossRefGoogle Scholar
  6. S. Borsanyi, G. Endrodi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti, K.K. Szabo, JHEP 08, 53 (2012)ADSCrossRefGoogle Scholar
  7. S. Borsanyi, Z. Fodor, C. Hoelbling, S.D. Katz, S. Krieg, K.K. Szabo, Phys. Lett. B 730, 99 (2014)ADSCrossRefGoogle Scholar
  8. E. Braaten, R.D. Pisarski, Nucl. Phys. B 337, 569 (1990); 339, 310 (1990)Google Scholar
  9. G.E. Brown, B.A. Gelman, M. Rho, Phys. Rev. Lett. 96, 132301 (2006)ADSCrossRefGoogle Scholar
  10. M. Cheng et al., Phys. Rev. D 81, 54504 (2010)ADSCrossRefGoogle Scholar
  11. M. Cheng, Phys. Rev. D 81 (2010)Google Scholar
  12. S. Datta, F. Karsch, P. Petreczky, I. Wetzorke, Phys. Rev. D 69, 94507 (2004)ADSCrossRefGoogle Scholar
  13. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965)zbMATHGoogle Scholar
  14. V.S. Filinov, Yu.B Ivanov, M. Bonitz, V.E Fortov, P.R Levashov. Phys. Lett. A 376, 1096 (2012)ADSCrossRefGoogle Scholar
  15. V.S. Filinov, V.E. Fortov, M. Bonitz, P.R. Levashov, JETP Lett. 74, 384 (2001)ADSCrossRefGoogle Scholar
  16. V.S. Filinov, H. Fehske, M. Bonitz, V.E. Fortov, P.R. Levashov, Phys. Rev. E 75, 036401 (2007)ADSCrossRefGoogle Scholar
  17. V.S. Filinov, M. Bonitz, Y.B. Ivanov, E.-M. Ilgenfritz, V.E. Fortov, Contrib. Plasma Phys. 55(2–3), 203 (2015)ADSCrossRefGoogle Scholar
  18. V.S. Filinov, M. Bonitz, YuB Ivanov, E.-M. Ilgenfritz, V.E. Fortov, Plasma Phys. Control Fusion 57, 44004 (2015)CrossRefGoogle Scholar
  19. V.S. Filinov, M. Bonitz, W. Ebeling, V.E. Fortov, Plasma Phys. Control Fusion 43, 743 (2001)ADSCrossRefGoogle Scholar
  20. A. Filinov, V. Golubnychiy, M. Bonitz et al., Phys. Rev. E 70, 46411 (2004)ADSCrossRefGoogle Scholar
  21. V.S. Filinov, M. Bonitz, W. Ebeling, V.E. Fortov, Plasma Phys. Control Fusion 43, 743–759 (2001)ADSCrossRefGoogle Scholar
  22. V.S. Filinov, V.E. YuB Ivanov, M. Fortov, P.R.Levashov Bonitz, Phys. Rev. C 87, 35207 (2013)ADSCrossRefGoogle Scholar
  23. V.S. Filinov, V.E. Fortov, M. Bonitz, D. Kremp, Phys. Lett. A 274, 228 (2000)ADSCrossRefGoogle Scholar
  24. V.S. Filinov, M. Bonitz, Y.B. Ivanov, V.V. Skokov, P.R. Levashov, V.E. Fortov, Contrib. Plasma Phys. 52, 135 (2012)ADSCrossRefGoogle Scholar
  25. V.S. Filinov, Y.B. Ivanov, M. Bonitz, P.R. Levashov, V.E. Fortov, Phys. Atom. Nucl. 74, 1364 (2011)ADSCrossRefGoogle Scholar
  26. V.S. Filinov, Y.B. Ivanov, M. Bonitz, P.R. Levashov, V.E. Fortov, Phys. Atom. Nucl. 75, 693 (2012)ADSCrossRefGoogle Scholar
  27. V.S. Filinov, M. Bonitz, Y.B. Ivanov, V.V. Skokov, P.R. Levashov, V.E. Fortov, Contrib. Plasma Phys. 49, 536 (2009)ADSCrossRefGoogle Scholar
  28. V.S. Filinov, M. Bonitz, Y.B. Ivanov, V.V. Skokov, P.R. Levashov, V.E. Fortov, Contrib. Plasma. Phys. 51, 322–327 (2011)ADSCrossRefGoogle Scholar
  29. Z. Fodor, S.D. Katz, Phys. Lett. B 534, 87 (2002); Z. Fodor, S.D. Katz, arXiv:0908.3341 [hep-ph]
  30. I.M. Gelfand, A.M. Yaglom, Uspekhi Mat. Nauk 11, 77 (1956)Google Scholar
  31. B.A. Gelman, E.V. Shuryak, I. Zahed, Phys. Rev. C 74, 44908 (2006); ibid. 74, 44909 (2006)Google Scholar
  32. I.S. Gradstein, I.M. Ryzik, Tables of Integrals, Sums, Series and Products, Moscow (Gos. Izd. Phys.-Math, Lit, 1963)Google Scholar
  33. P. Hartmann, Z. Donko, P. Levai, G.J. Kalman, J. Phys. A 42, 214029 (2006); Nucl. Phys. A 774, 881–884 (2006)Google Scholar
  34. A.L. Harvey, Phys. Rev. D 6, 1474 (1972)ADSCrossRefGoogle Scholar
  35. M. Hofmann, M. Bleicher, S. Scherer, L. Neise, H. Stoecker, W. Greiner, Phys. Lett. B 478, 161 (2000)ADSCrossRefGoogle Scholar
  36. K. Huang, Statistical Mechanics (Wiley, New York, 1963)Google Scholar
  37. K. Johnson, Ann. Phys. 192, 104 (1989)ADSCrossRefGoogle Scholar
  38. F. Karsch, M. Kitazawa, Phys. Rev. D 80, 56001 (2009)ADSCrossRefGoogle Scholar
  39. G. Kelbg, Quantenstatistik der Gase mit Coulombwechselwirkung. Ann. Physik (Leipzig) 12, 219–224, 354–360 (1963)Google Scholar
  40. P.F. Kelly, Q. Liu, C. Lucchesi, C. Manuel, Phys. Rev. Lett. 72, 3461 (1994a)Google Scholar
  41. P.F. Kelly, Q. Liu, C. Lucchesi, C. Manuel, Phys. Rev. D 50, 4209 (1994b)Google Scholar
  42. V. Koch, A. Majumder, J. Randrup, Phys. Rev. Lett. 95, 182301 (2005)ADSCrossRefGoogle Scholar
  43. A.S. Larkin, V.S. Filinov, Phys. Lett. A 378, 1876 (2014)ADSMathSciNetCrossRefGoogle Scholar
  44. M. Le Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, 1996)CrossRefGoogle Scholar
  45. J. Liao, E.V. Shuryak, Phys. Rev. D 73, 14509 (2006)ADSCrossRefGoogle Scholar
  46. D.F. Litim, C. Manuel, Phys. Rev. Lett. 82, 4981 (1999); Nucl. Phys. B 562, 237 (1999); Phys. Rev. D 61, 125004 (2000). Phys. Rep. 364, 451 (2002)Google Scholar
  47. W. Lucha, F.F. Schoberl, D. Gromes, Phys. Rep. 200, 127 (1991)ADSCrossRefGoogle Scholar
  48. W. Lucha, F.F. Schoberl, Int. J. Mod. Phys. A 7, 6431 (1992)ADSCrossRefGoogle Scholar
  49. M.S. Marinov, Phys. Rep. 60, 1 (1980)ADSCrossRefGoogle Scholar
  50. T.D. Newton, E.P. Wigner, Rev. Mod. Phys. 21, 400 (1949)ADSCrossRefGoogle Scholar
  51. P. Petreczky, F. Karsch, E. Laermann, S. Stickan, I. Wetzorke, Nucl. Phys. Proc. Suppl. 106, 513 (2002)ADSCrossRefGoogle Scholar
  52. R.D. Pisarski, Phys. Rev. Lett. 63, 1129 (1989)ADSCrossRefGoogle Scholar
  53. G.M. Prosperi, M. Raciti, C. Simolo, Prog. Part. Nucl. Phys. 58, 387 (2007)ADSCrossRefGoogle Scholar
  54. Y.B. Rumer, A.I. Fet, Group Theory and Quantum Fields (Nauka, Moscow, 1977)Google Scholar
  55. E.E. Salpeter, H.A. Bethe, Phys. Rev. 84, 1232 (1951)ADSCrossRefGoogle Scholar
  56. E.E. Salpeter, Phys. Rev. 87, 328 (1952)ADSCrossRefGoogle Scholar
  57. J. Schleede, A. Filinov, M. Bonitz, H. Feshkse, Contrib. Plasma Phys. 52, 819 (2012)ADSCrossRefGoogle Scholar
  58. E.V. Shuryak, I. Zahed, Phys. Rev. C 70, 21901 (2004). Phys. Rev. D 70, 54507 (2004)Google Scholar
  59. E. Shuryak, Prog. Part. Nucl. Phys. 62, 48 (2009); ibid. 53, 273 (2004)Google Scholar
  60. E.V. Shuryak, Prog. Part. Nucl. 62, 48 (2009)ADSCrossRefGoogle Scholar
  61. J. Schukraft, (2011). arXiv:1112.0550, arXiv:hep-ex
  62. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Izd. Inostr. Lit, Moscow, 1963)zbMATHGoogle Scholar
  63. C. Shen, U. Heinz, Phys. Rev. C 85, 54902 (2012)ADSCrossRefGoogle Scholar
  64. D.V. Shirkov, I.L. Solovtsov, Phys. Rev. Lett. 79, 1209 (1997); Nucl. Phys. Proc. Suppl. 64, 106 (1998)Google Scholar
  65. S.K. Wong, Nuovo Cimento A 65, 689 (1970)ADSCrossRefGoogle Scholar
  66. V.I. Yukalov, E.P. Yukalova, Physica A 243, 382 (1997); Fiz. Elem. Chastits At. Yadra 28, 89 (1997)Google Scholar
  67. S. Cho, I. Zahed, Phys. Rev. C 79, 44911 (2009); ibid. 80, 14906 (2009); ibid. 82, 54907 (2010); ibid. 82, 64904 (2010); ibid. 82, 44905 (2010); K. Dusling, I. Zahed. Nucl. Phys. A 833, 172 (2010)Google Scholar
  68. V.M. Zamalin, G.E. Norman, U.S.S.R. Comp, Math. Math. Phys. 13, 169 (1973)CrossRefGoogle Scholar
  69. V.M. Zamalin, G.E. Norman, V.S. Filinov, The Monte Carlo Method in Statistical Thermodynamics (Nauka, Moscow, 1977). (in Russian)Google Scholar
  70. B.V. Zelener, G.E. Norman, V.S. Filinov, Perturbation Theory and Pseudopotential in Statistical Thermodynamics (Nauka, Moscow, 1981). (in Russian)Google Scholar
  71. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Plenum Press, New York London, 1974)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Werner Ebeling
    • 1
    Email author
  • Vladimir E. Fortov
    • 2
  • Vladimir Filinov
    • 3
  1. 1.Institut für PhysikHumboldt Universität BerlinBerlinGermany
  2. 2.Russian Academy of SciencesMoscowRussia
  3. 3.Joint Institute for High TemperaturesRussian Academy of SciencesMoscowRussia

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