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1
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85038919265
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Quark Matter ’96, Nucl. Phys. A610 (1996)
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Quark Matter ’96, Nucl. Phys. A610 (1996)
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2
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85038886236
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LATTICE ’96, Nucl. Phys. B (Proc. Suppl.) 53 (1997)
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LATTICE ’96, Nucl. Phys. B (Proc. Suppl.) 53 (1997).
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7
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0003664044
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World Scientific, Singapore
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K. Rajagopal, in Quark-Gluon Plasma 2, edited by R. Hwa (World Scientific, Singapore, 1995).
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(1995)
Quark-Gluon Plasma 2
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Rajagopal, K.1
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19
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85038957303
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K. Ogure and J. Sato, hep-ph/9802418 (1998) and references therein.
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Ogure, K.1
Sato, J.2
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21
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36149006782
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For applications of the mean-field method to field theories, see, e.g., Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)
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(1961)
Phys. Rev.
, vol.122
, pp. 345
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Nambu, Y.1
Jona-Lasinio, G.2
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23
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85038915363
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Since the number of works related to OPT is enormous, we quote only two books which contain the original references: G. A. Arteca, F. M. Fernández, and E. A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics, (Springer-Verlag, Berlin, 1990)
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Since the number of works related to OPT is enormous, we quote only two books which contain the original references: G. A. Arteca, F. M. Fernández, and E. A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics, (Springer-Verlag, Berlin, 1990)
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29
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0001645449
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[In the first reference, OPT at finite (Formula presented) was examined with (Formula presented) being a small perturbation, which is in contrast with our approach.] See also G. A. Hajj and P. M. Stevenson, Phys. Rev. D 37, 413 (1988).
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(1988)
Phys. Rev. D
, vol.37
, pp. 413
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Hajj, G.A.1
Stevenson, P.M.2
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35
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7244233047
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Phys. Rev. DP. Arnold and C.-X. Zhai, 50, 7603 (1994)
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(1994)
Phys. Rev. D
, vol.50
, pp. 7603
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Arnold, P.1
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39
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85038954163
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If we explicitly write (Formula presented) in Eq. (4), it appears as (Formula presented) Therefore, the loop expansion by (Formula presented) at finite (Formula presented) does not coincide with the (Formula presented) expansion. The expansion by (Formula presented) should be regarded as a steepest descent evaluation of the functional integral 17
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If we explicitly write (Formula presented) in Eq. (4), it appears as (Formula presented) Therefore, the loop expansion by (Formula presented) at finite (Formula presented) does not coincide with the (Formula presented) expansion. The expansion by (Formula presented) should be regarded as a steepest descent evaluation of the functional integral 17.
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44
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0000884158
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Chiral Dynamics (Gordon and Breach, New York, 1972)
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B. W. Lee, Nucl. Phys. B9, 649 (1969); NUPBBOChiral Dynamics (Gordon and Breach, New York, 1972).
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(1969)
Nucl. Phys.
, vol.B9
, pp. 649
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Lee, B.W.1
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46
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85038890308
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This point was first recognized in 14
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This point was first recognized in 14.
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47
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85038891405
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At finite (Formula presented) or chemical potential, only the rotational symmetry in space is preserved in the rest frame of the heat bath or matter. Therefore, (Formula presented) in general
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At finite (Formula presented) or chemical potential, only the rotational symmetry in space is preserved in the rest frame of the heat bath or matter. Therefore, (Formula presented) in general.
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50
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85038916768
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Although (Formula presented) at high (Formula presented) coincides with the Debye screening mass for (Formula presented) they could be different in higher orders: Physical Debye mass is, in general, a function of (Formula presented)
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Although (Formula presented) at high (Formula presented) coincides with the Debye screening mass for (Formula presented) they could be different in higher orders: Physical Debye mass is, in general, a function of (Formula presented)
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51
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85038904710
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this case, (Formula presented) at the stationary point of the thermal effective potential
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In this case, (Formula presented) at the stationary point of the thermal effective potential.
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53
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85038937016
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See, e.g., C. Itzykson and J-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1985)
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See, e.g., C. Itzykson and J-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1985)
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55
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0001660516
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See the following papers and the references quoted therein for the breakdown of the NG theorem in self-consistent methods and for attempts to cure the problem: A. Okopińska, Phys. Lett. B 375, 213 (1996)
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(1996)
Phys. Lett. B
, vol.375
, pp. 213
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Okopińska, A.1
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60
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0001435921
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Another interesting issue is the spectral change of vector mesons: R. D. Pisarski, Phys. Lett. 110B, 155 (1982)
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(1982)
Phys. Lett.
, vol.110B
, pp. 155
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Pisarski, R.D.1
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74
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0000132156
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J. Randrup, Phys. Rev. D 55, 1188 (1997) and references therein.
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(1997)
Phys. Rev. D
, vol.55
, pp. 1188
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Randrup, J.1
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75
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85038957673
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present paper, (Formula presented) and the sign of (Formula presented) are defined differently from those in 34. Also (Formula presented) in 34 should be considered as an unrenormalized parameter, while (Formula presented) in the present paper is a renormalized one
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In the present paper, (Formula presented) and the sign of (Formula presented) are defined differently from those in 34. Also (Formula presented) in 34 should be considered as an unrenormalized parameter, while (Formula presented) in the present paper is a renormalized one.
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84
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0002029232
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Phys. Lett. BM. Bando, T. Kugo, N. Maekawa, and H. Nakano, 301, 83 (1993)
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(1993)
Phys. Lett. B
, vol.301
, pp. 83
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Bando, M.1
Kugo, T.2
Maekawa, N.3
Nakano, H.4
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86
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0003984846
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Cambridge University Press, Cambridge, England
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M. Le Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, England, 1996).
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(1996)
Thermal Field Theory
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Le Bellac, M.1
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91
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0003500871
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Addison-Wesley, New York
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We have studied the free energy as a function of (Formula presented) near the chiral limit and found that it has a discontinuity at a certain temperature between (Formula presented) and (Formula presented) This is another sign that the first order nature is an artifact of the approximation. [Remember that the free energy must be a continuous function of (Formula presented) irrespective of the order of the phase transition: see, e.g., N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, New York, 1992).]
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(1992)
Lectures on Phase Transitions and the Renormalization Group
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Goldenfeld, N.1
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98
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0542370287
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A preliminary version of this study has been reported in S. Chiku, Prog. Theor. Phys. Suppl. 129, 91 (1998).
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(1998)
Prog. Theor. Phys. Suppl.
, vol.129
, pp. 91
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Chiku, S.1
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102
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0031231905
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P. Rehberg, Yu. I. Kalinovskii, and D. Blaschke, Nucl. Phys. A622, 478 (1997). In this paper, the mode couplings are not taken into account.
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(1997)
Nucl. Phys.
, vol.A622
, pp. 478
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Rehberg, P.1
Blaschke, D.2
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104
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0000915753
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See also T. Hatsuda, Phys. Rev. D 56, 8111 (1997) and references therein.
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(1997)
Phys. Rev. D
, vol.56
, pp. 8111
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Hatsuda, T.1
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