Prog. Theor. Phys. Vol. 71 No. 6 (1984) pp. 1332-1345

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A Self-Consistent Mean-Field Approach to the Dynamical Symmetry Breaking

— The Effective Potential of the Nambu and Jona-Lasinio Model —

Teiji Kunihiro and Tetsuo Hatsuda^*

Department of Natural Sciences, Ryukoku University, Kyoto 612
^*Department of Physics, Kyoto University, Kyoto 606

(Received August 4, 1983)

Abstract:

The dynamical symmetry breaking phenomena in the Nambu and Jona-Lasinio model are reexamined in the framework of a self-consistent mean-field (SCMF) theory. First, we formulate the SCMF theory in a lucid manner based on a successful decomposition on the Lagrangian into semiclassical and residual interaction parts by imposing a condition that “the dangerous term” in Bogoliubov's sense should vanish. Then, we show that the difference of the energy density between the super and normal phases, the correct expression of which the original authors failed to give, can be readily obtained by applying the SCMF theory. Furthermore, it is shown that the expression thus obtained is identical to that of the effective potential (E. P.) given by the path-integral method with an auxiliary field up to the one loop order in the loop expansion, then one finds a new and simple way to get the E. P. Some numerical results of the E. P. and the dynamically generated mass of fermion are also shown. As another demonstration of the powerfulness of the SCMF theory, we derive, in the Appendix, the energy density of the O(N)-φ⁴ model including the higher order corrections in the sense of large N expansion.

URL : http://ptp.ipap.jp/link?PTP/71/1332/
DOI : 10.1143/PTP.71.1332

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Citing Article(s) :

Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 765-781 :
Soft Modes Associated with Chiral Symmetry Breaking

Tetsuo Hatsuda and Teiji Kunihiro
Progress of Theoretical Physics Vol. 75 No. 2 (1986) pp. 301-318 :
Effects Finite Density on Chiral Domain-Wall in Neutron and Quark Matter

Tetsuo Hatsuda
Progress of Theoretical Physics Supplement No.91 (1987) pp. 284-298 :
Pion and σ-Meson at Finite Temperature

Tetsuo Hatsuda and Teiji Kunihiro
Progress of Theoretical Physics Supplement No.120 (1995) pp. 75-93 :
Chiral Symmetry and Scalar Meson in Hadron and Nuclear Physics

Teiji Kunihiro