Abstract
We describe how the thermal counterpart of a vacuum two-point function may be obtained in the real time formalism in a simple way by using directly the 2×2 matrices that different elements acquire in this formalism. Using this procedure we calculate the analytic (single component) thermal amplitude for the pion pole term in the ensemble average of two axial-vector currents to two loops in chiral perturbation theory. The general expressions obtained for the effective mass and the decay constants of the pion are evaluated in the chiral and the non-relativistic limits.
Similar content being viewed by others
References
G.W. Semenoff, H. Umezawa, Nucl. Phys. B 220, 196 (1983)
A.J. Niemi, G.W. Semenoff, Ann. Phys. (New York) 152, 105 (1984)
For a review see C.G. van Weert, Phys. Rep. 145, 141 (1987)
J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984)
J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)
J. Gasser, H. Leutwyler, Phys. Lett. B 184, 83 (1987)
J. Goity, H. Leutwyler, Phys. Lett. B 228, 517 (1989)
A. Schenk, Phys. Rev. D 47, 5138 (1993)
C. Song, Phys. Rev. D 49, 1556 (1994)
A. Ayala, S. Sahu, Phys. Rev. D 62, 056007 (2000)
D. Toublan, Phys. Rev. 56, 5629 (1997)
P. Gerber, H. Leutwyler, Nucl. Phys. B 321, 387 (1989)
H. Leutwyler, Phys. Rev. D 49, 3033 (1994)
R.D. Pisarski, M. Tytgat, Phys. Rev. D 54, 2989 (1996)
G. Ecker, in Chiral Dynamics: Theory and Experiment, ed. by A.M. Bernstein, D. Drechsel, T. Walcher (Springer, 1997)
G. Colangelo, J. Gasser, H. Leutwyler, Nucl. Phys. B 603, 125 (2001)
G. Ecker, J. Gasser, A. Pich, E. de Rafael, Nucl. Phys. B 321, 311 (1989)
G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Phys. Lett. B 223, 425 (1989)
H. Leutwyler, A.V. Smilga, Nucl. Phys. B 342, 302 (1990)
Y. Fujimoto, H. Matsumoto, H. Umezawa, I. Ojima, Phys. Rev. D 30, 1400 (1984)
R.L. Kobes, G.W. Semenoff, Nucl. Phys. B 260, 714 (1985)
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS
11.10.Wx; 12.38.Mh; 12.39.Fe
Rights and permissions
About this article
Cite this article
Mallik, S., Sarkar, S. Pion propagation in real time field theory at finite temperature. Eur. Phys. J. C 49, 755–766 (2007). https://doi.org/10.1140/epjc/s10052-006-0150-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-006-0150-1