Damping rate of a fast fermion in hot QED

R. Baier; R. Kobes

doi:10.1103/PhysRevD.50.5944

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Damping rate of a fast fermion in hot QED

R. Baier

R. Kobes

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030
Fakultät für Physik, Universität Bielefeld, D-33501 Bielefeld, Germany

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030
Laboratoire de Physique Théorique, ENSLAPP, BP110, F-74941 Annecy-le-Vieux, France

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Phys. Rev. D 50, 5944 – Published 1 November, 1994

DOI: https://doi.org/10.1103/PhysRevD.50.5944

Abstract

The self-consistent determination of the damping rate of a fast moving fermion in a hot QED plasma is reexamined. We argue how a detailed investigation of the analytic properties of the retarded fermion Green’s function motivated by the cutting rules at finite temperature may resolve ambiguities related to the proper definition of the mass-shell condition.

References (35)

R. D. Pisarski, Phys. Rev. Lett. 63, 1129 (1989); E. Braaten and R. D. Pisarski (unpublished).
V. V. Lebedev and A. V. Smilga, Ann. Phys. (N.Y.) 202, 229 (1990); Phys. Lett. B 253, 231 (1991) Phys. Lett. A 181, 187 (1992).
C. P. Burgess and A. L. Marini, Phys. Rev. D 45, 1297 (1992); A. Rebhan, ibid. 46, 482 (1992).
T. Altherr, E. Petitgirard, and T. del Rio Gaztelrrutia, Phys. Rev. D 47, 703 (1993).
H. Nakkagawa, A. Niégawa and B. Pire, Phys. Lett. B 294, 396 (1992); Can. J. Phys. 71, 269 (1993).
R. Baier, H. Nakkagawa and A. Niégawa, Can. J. Phys. 71, 205 (1993).
H. Heiselberg and C. J. Pethick, Phys. Rev. D 47, 12769 (1993).
A. V. Smilga, Yad. Fiz. 57, 550 (1994); Phys. At. Nucl. (to be published).
R. D. Pisarski, Phys. Rev. D 47, 5589 (1993).
S. Peigné, E. Pilon and D. Schiff, Z. Phys. C 60, 455 (1993).
R. D. Pisarski, Can. J. Phys. 71, 280 (1993).
E. Braaten and R. D. Pisarski, Nucl. Phys. B337, 569 (1990); ibid. B339, 310 (1990).
J. Frenkel and J. C. Taylor, Nucl. Phys. B334, 199 (1990).
It was already remarked by Pisarski citer9,r11, Smilga citer8, and Chu and Umezawa citer14 that this pole may not be present on the first Riemann sheet.
H. Chu and H. Umezawa, ``A unified formalism of thermal quantum field theory, " University of Alberta report (unpublished).
R. Mills, Propagators for Many Particle Systems (Gordon and Breach, New York, 1969).
A. L. Fetter and J. D. Walecka, Quantum Theory of Many Particle Systems (McGraw Hill, New York, 1971).
N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987). Earlier work is quoted in this review paper.
E. S. Fradkin, Proc. Lebedev Phys. Inst. 29, 6 (1965).
N. P. Landsman, Ann. Phys. (N.Y.) 186, 141 (1988).
R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S Matrix (Cambridge University Press, Cambridge, 1966).
C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw Hill, New York, 1980).
R. D. Pisarski, Physica A 158, 146 (1989), and references to earlier work quoted therein.
R. Kobes, G. Kunstatter and A. Rebhan, Phys. Rev. Lett. 64, 2992 (1990); Nucl. Phys. B355, 1 (1991).
H. A. Weldon, Phys. Rev. D 28, 2007 (1983).
R. L. Kobes and G. W. Semenoff, Nucl. Phys. B260, 714 (1985); ibid. B272, 329 (1986).
J. F. Donoghue and B. R. Holstein, Phys. Rev. D 28, 340 (1983).
E. Petitgirard, Z. Phys. C 54, 673 (1994).
The relevant density is the one related to the Dirac operator, usually denoted by $ρ_{1}$ citer21.
Note that for $G^{R}$ of Eq. ( refa4) and hat $G^{R}$ of Eq. ( ref7) we have Im hat $G^{R}$ ( $p_{0}$ ,p) doteq 2π ${EImG}^{R}$ ( $p_{0}$ ,p).
A. V. Selikhov and M. Gyulassy, Phys. Lett. B 316, 373 (1993).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1965).
A. Niégawa, Osaka Report No. OCU PHYS 154, 1994 (unpublished).
M. E. Carrington, Phys. Rev. D 48, 3836 (1993).
U. Kraemmer, A. K. Rebhan, and H. Schulz, DESY Report No. DESY 94 034, 1994 (unpublished).

[c1] R. D. Pisarski, Phys. Rev. Lett. 63, 1129 (1989); E. Braaten and R. D. Pisarski (unpublished).

[c2] V. V. Lebedev and A. V. Smilga, Ann. Phys. (N.Y.) 202, 229 (1990); Phys. Lett. B 253, 231 (1991) Phys. Lett. A 181, 187 (1992).

[c3] C. P. Burgess and A. L. Marini, Phys. Rev. D 45, 1297 (1992); A. Rebhan, ibid. 46, 482 (1992).

[c4] T. Altherr, E. Petitgirard, and T. del Rio Gaztelrrutia, Phys. Rev. D 47, 703 (1993).

[c5] H. Nakkagawa, A. Niégawa and B. Pire, Phys. Lett. B 294, 396 (1992); Can. J. Phys. 71, 269 (1993).

[c6] R. Baier, H. Nakkagawa and A. Niégawa, Can. J. Phys. 71, 205 (1993).

[c7] H. Heiselberg and C. J. Pethick, Phys. Rev. D 47, 12769 (1993).

[c8] A. V. Smilga, Yad. Fiz. 57, 550 (1994); Phys. At. Nucl. (to be published).

[c9] R. D. Pisarski, Phys. Rev. D 47, 5589 (1993).

[c10] S. Peigné, E. Pilon and D. Schiff, Z. Phys. C 60, 455 (1993).

[c11] R. D. Pisarski, Can. J. Phys. 71, 280 (1993).

[c12] E. Braaten and R. D. Pisarski, Nucl. Phys. B337, 569 (1990); ibid. B339, 310 (1990).

[c13] J. Frenkel and J. C. Taylor, Nucl. Phys. B334, 199 (1990).

[c14] It was already remarked by Pisarski citer9,r11, Smilga citer8, and Chu and Umezawa citer14 that this pole may not be present on the first Riemann sheet.

[c15] H. Chu and H. Umezawa, ``A unified formalism of thermal quantum field theory, " University of Alberta report (unpublished).

[c16] R. Mills, Propagators for Many Particle Systems (Gordon and Breach, New York, 1969).

[c17] A. L. Fetter and J. D. Walecka, Quantum Theory of Many Particle Systems (McGraw Hill, New York, 1971).

[c18] N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987). Earlier work is quoted in this review paper.

[c19] E. S. Fradkin, Proc. Lebedev Phys. Inst. 29, 6 (1965).

[c20] N. P. Landsman, Ann. Phys. (N.Y.) 186, 141 (1988).

[c21] R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S Matrix (Cambridge University Press, Cambridge, 1966).

[c22] C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw Hill, New York, 1980).

[c23] R. D. Pisarski, Physica A 158, 146 (1989), and references to earlier work quoted therein.

[c24] R. Kobes, G. Kunstatter and A. Rebhan, Phys. Rev. Lett. 64, 2992 (1990); Nucl. Phys. B355, 1 (1991).

[c25] H. A. Weldon, Phys. Rev. D 28, 2007 (1983).

[c26] R. L. Kobes and G. W. Semenoff, Nucl. Phys. B260, 714 (1985); ibid. B272, 329 (1986).

[c27] J. F. Donoghue and B. R. Holstein, Phys. Rev. D 28, 340 (1983).

[c28] E. Petitgirard, Z. Phys. C 54, 673 (1994).

[c29] The relevant density is the one related to the Dirac operator, usually denoted by $ρ_{1}$ citer21.

[c30] Note that for $G^{R}$ of Eq. ( refa4) and hat $G^{R}$ of Eq. ( ref7) we have Im hat $G^{R}$ ( $p_{0}$ ,p) doteq 2π ${EImG}^{R}$ ( $p_{0}$ ,p).

[c31] A. V. Selikhov and M. Gyulassy, Phys. Lett. B 316, 373 (1993).

[c32] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1965).

[c33] A. Niégawa, Osaka Report No. OCU PHYS 154, 1994 (unpublished).

[c34] M. E. Carrington, Phys. Rev. D 48, 3836 (1993).

[c35] U. Kraemmer, A. K. Rebhan, and H. Schulz, DESY Report No. DESY 94 034, 1994 (unpublished).

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