2004 Fiscal Year Final Research Report Summary
Analysis of the chiral symmetry breaking by non-perturbative renormalization group
| Project/Area Number |
13440076
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
素粒子・核・宇宙線
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| Research Institution | Kanazawa University |
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Principal Investigator |
AOKI Ken-Ichi Kanazawa University, Graduate School of Science, Professor, 自然科学研究科, 教授 (00150912)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Tsuneo Kanazawa University, Graduate School of Science, Professor, 総合メディア基盤センター, 教授 (60019502)
TERAO Haruhiko Kanazawa University, Graduate School of Science, Associate Professor, 自然科学研究科, 助教授 (40192653)
IZUBUCHI Taku Kanazawa University, Graduate School of Science, Assistant, 自然科学研究科, 助手 (60324068)
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| Project Period (FY) |
2001 – 2004
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| Keywords | non-perturbative / renormalization group / chiral symmetry / gauge theory / tunneling / spontaneous symmetry breaking / effective interactions / phase structure |
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| Research Abstract |
The spontaneous breakdown of the chiral symmetry and its phase structure due to the strong interaction is an important issue for understanding the origin of the mass of elementary particles and for the basic properties of states at high temperature and at high density. This research project serves to develop the analysis method of the low energy effective theory of the quantum chromodynamics by using the non-perturbative renormalization group. We calculate the effective potential to describe the spontaneous breakdown of the chiral symmetry and investigate the basic techniques to analyze the phase structures.
In the medium of the non-zero density of the baryon number, the previously adopted way of finding the spontaneous symmetry breaking of the chiral symmetry is found to be incorrect. It is necessary to incorporate the auxiliary fields to describe the correct renormalization group flows. Also we need the finite density corrections to the QCD beta function. These are the next subjects t
… More
o be attacked.
In order to deeply understand the fundamental issues of the dynamics of the spontaneous symmetry breakdown, we apply the non-perturbative renormalization group method to the quantum mechanics of one-dimensional potential problem including the so-called double well potential. We develop the decimation renormalization group method and successfully calculate the free energy with quite a high precision. Also we attacked the dissipative quantum systems by this method to evaluate the critical dissipation causing the quantum to classical phase transition. Our results are different quantitatively from the previous calculations using the instanton method with the perturbation theory. Detailed comparison will be in order.
Using the Monte Carlo simulation of the lattice QCD, some important features are obtained about the high temperature and finite densiy QCD, which have been carried out mainly by co-investigators. These basic results will serve for future analyses for the high density phase transition and the color super conductivity transitions. Less
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