A Self-Consistent Mean-Field Approach to the Dynamical Symmetry Breaking : The Effective Potential of the Nambu and Jona-Lasinio Model : Particles and Fields

概要

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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 of 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)-φ^4 model including the higher order corrections in the sense of large N expansion.
理論物理学刊行会の論文
1984-06-25