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References
For some of the material in this chapter, the following books may be useful: M. Le Bellac, Thermal Field Theory, Cambridge University Press (2000); A. Das, Finite Temperature Field Theory, World Scientific Pub. Co. (1997); J.I. Kapusta, Finite Temperature Field Theory, Cambridge University Press (1994).
For a general reference on the use of the density matrix, see R.P. Feynman, Statistical Mechanics, Addison-Wesley Pub. Co. (1972).
The KMS condition is due to R. Kubo, J. Phys. Soc. Japan 12, 570 (1957); P.C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959).
The screening of electrostatic fields goes back to P. Debye’s work on electrolytes in the 1920s. The calculation using thermal photon propagator is due to V.P. Silin, Sov. J. Phys. JETP 11, 1136 (1960); V.N. Tsytovich, Sov. Phys. JETP, 13, 1249(1961); O.K. Kalashnikov and V.V. Klimov, Sov. J. Nucl. Phys., 31, 699 (1980); V.V. Klimov, Sov. J. Nucl. Phys. 33, 934 (1981); Sov. Phys. JETP 55, 199 (1982); H.A. Weldon, Phys. Rev. D26, 1394 (1982).
Screening of nonabelian gauge fields, by isolating hard thermal loops, was done by R. Pisarski, Physica A158, 246 (1989); Phys. Rev. Lett. 63, 1129 (1989); E. Braaten and R. Pisarski, Phys. Rev. D42, 2156 (1990); Nucl. Phys. B337, 569 (1990); ibid. B339, 310 (1990); Phys. Rev. D45, 1827 (1992).
Calculations of the effective action for screening are also given in J. Frenkel and J.C. Taylor, Nucl. Phys. B334, 199 (1990); J.C. Taylor and S.M.H. Wong, Nucl. Phys. B346, 115 (1990); R. Efraty and V.P. Nair, Phys. Rev. Lett. 68, 2891 (1992); Phys. Rev. D47, 5601 (1993). We have followed the last reference in our presentation.
A kinetic equation approach has been used by P.F. Kelly et al, Phys. Rev. Lett. 72, 3461 (1994); Phys. Rev. D50, 4209 (1994).
Kubo’s paper in reference 3 gives the Abelian Kubo formula.
For the calculation of the imaginary part of Γ we follow R. Jackiw and V.P. Nair, Phys. Rev. D48, 4991 (1993); Related work is also given by J.P. Blaizot and E. Iancu, Nucl. Phys. B390, 589 (1993); Phys. Rev. Lett. 70, 3376 (1993).
For screening at high densities, see C. Manuel, Phys. Rev. D53, 5866 (1996); G. Alexanian and V.P. Nair, Phys. Lett. B390, 370 (1997).
A recent review on screening effects for gauge fields is U. Kraemmer and A. Rebhan, Rep. Prog. Phys. 67, 351 (2004).
The method of time-contour is due to J. Schwinger, J. Math. Phys. 2, 407 (1961); P.M. Bakshi and K. Mahanthappa, J. Math. Phys. 4, 1 (1963); ibid. 4, 12 (1963); L.V. Keldysh, Sov. Phys. JETP 20, 1018 (1964).
The Kadanoff-Baym equations are in L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, W.A. Benjamin, Inc. (1962).
A general reference on quantum kinetic theory is S.R. De Groot, W.A. van Leeuwen and Ch. G. van Weert, Relativistic Kinetic Theory, North-Holland/ Elsevier (1980).
Imaginary time Green’s functions were introduced by T. Matsubara, Prog. Theor. Phys. 14, 351 (1955).
For relativistic field theories, this formalism was used by D.A. Kirzhnits and A.D. Linde, Phys. Lett. B42, 471 (1972); Ann. Phys. 101, 195 (1976); L. Dolan and R. Jackiw, Phys. Rev. D9, 3320 (1974); S. Weinberg, Phys. Rev. D9, 3357 (1974). These papers also discuss symmetry restoration at high temperatures.
The observation that the ghosts must obey periodic boundary condition is due to C. Bernard, Phys. Rev. D9, 3312 (1974).
The situation regarding the order of the phase transition in the standard model, as well as the O(N) model at small N, is not completely satisfactory yet; for a recent review, see P. Arnold, Lecture at Quarks’ 94, Russia, 1994, http://arXiv.org/hep-ph/9410294.
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(2005). Finite temperature and density. In: Quantum Field Theory. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-25098-0_18
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