Spontaneous Breaking of Chiral Symmetry in a Vector-Gluon Model
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概要
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Solutions of the self-consistent equation for fermion propagator in a vector- gluon model are fully examined. The equation is characterized by a set of parameters, i.e., the coupling constant g, the bare mass of the fermion m_0 and the cutoff Λ. It is proved that with a suitable gauge chosen, the equation without cutoff has solutions only in the case m_0=0. It is then shown that, if g^2/4π < (16/33)^2π, the freedom of fixing the mass scale since the gluon mass is chosen to be non-vanishing. When the cutoff is introduced, the equation has a unique solution for g^2/4π < π/4. In this case, however, β turns out to be identically zero if we put m_0=0, which means that any "superconducting" solutions do not exist for such a value of g irrespective of cutoff momentum; that is, there are no Nambu-Goldstone bosons. When g^2 is large enough, such a "superconducting" solution does exist in the model in which the vector part of the inverse fermion propagator is identically set equal to unity. Furthermore the existence of many "superconducting" solutions is inferred in this model. It is also found that in the region g^2/4π < 8π, the "normal-state" solution for the equation without cutoff, even if it existed, should necessarily have an unphysical singularity. This fact implies that the "normal-state" solution becomes unstable for a sufficiently large value of g^2.
- 理論物理学刊行会の論文
- 1974-10-25
著者
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NAKAJIMA Hideo
Department of Information Systems Science, Utsunomiya University
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MASKAWA Toshihide
Institute for Nuclear Study, University of Tokyo
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MASKAWA Toshihide
Research Institute for Fundamental Physics Kyoto University
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Maskawa Toshihide
Department Of Physics Kyoto Sangyo University
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NAKAJIMA Hideo
Research Institute for Fundamental Physics, Kyoto University
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Nakajima Hideo
Department Of Engineering Mathematics Faculty Of Engineering Utsunomiya University
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NAKAJIMA Hiroaki
Department of Physics, Chuo University
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NAKAJIMA Hideo
Laboratory of Applied Mathematics and Mathematical Physics Department of Information Science, Utsunomiya University
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NAKAJIMA HIDEO
Deparment of Plastic and Reconstructive Surgery, School of Medicine, Keio University
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