Renormalization in the Gauged Nambu-Jona-Lasinio Model : Particles and Fields

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概要

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• Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure Nambu-Jona-Lasinio model is not renormalizable, presence of the gauge interaction makes it possible that the theory is renormalized as an interacting continuum theory at the critical line in the ladder approximation. Extra higher dimensional operators ("counter terms") are not needed for the theory to be renormalized. By virtue of the effective potential approach, the renormalization ("symmetric renormalization") is performed in a phaseindependent manner both for the symmetric and the spontaneously broken phase of the chiral symmetry. We explicitly obtain β function having a nontrivial ultraviolet fixed line for the renormalized coupling as well as the bare one. In both phases the anomalous dimension is very large (≥1) without discontinuity across the fixed line. Operator product expansion is explicitly constructed, which is consistent with the large anomalous dimension owing to the appearance of the nontrivial extra power behavior in the Wilson coefficient for the unit operator. The symmetric renormalization breaks down at the critical gauge coupling, which is cured by the generalized renormalization scheme ("M^^--dependent renormalization"). Also emphasized is the formal resemblance to the four-fermion theory in less than four dimensions which is renomalizable in 1/N expansion.

• 理論物理学刊行会の論文
• 1993-06-25

著者

• YAMAWAKI Koichi

  Department of Physics, Nagoya University

• KONDO Kei-ichi

  Department of Urology and Molecular Genetics, Yokohama City University Graduate School of Medicine

• Kondo K

  Chiba Univ. Chiba Jpn

• 山脇 幸一

  Department Of Physics Nagoya University

• Yamawaki Koichi

  Department Of Physics Kyoto University

• Kondo Kei-ichi

  Department Of Physic Nagoya University

• TANABASHI Masaharu

  National Laboratory for High Energy Physics (KEK)

• Tanabashi M

  Tohoku Univ. Sendai Jpn

• KONDO Kei-ichi

  Department of Physics, Nagoya University

• KONDO Kei-ichi

  Department of Physics, University of Tokyo : the Japan Society for the Promotion of Sciences. : Department of Physics, Nagoya University

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