2005 Fiscal Year Final Research Report Summary
Wide applications of the renormalization group
| Project/Area Number |
14340077
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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 | Kobe University |
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Principal Investigator |
SONODA Hidenori Kobe University, Physics Department, Assoc. Professor., 理学部, 助教授 (20291966)
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| Co-Investigator(Kenkyū-buntansha) |
LIM C.s. Kobe University, Physics Department, Professor, 理学部, 教授 (80201870)
HARIMA Hisatomo Kobe University, Physics Department, Professor, 理学部, 教授 (50211496)
KUBOKI Kazuhiro Kobe University, Physics Department, Assoc. Professor, 理学部, 助教授 (50231296)
NISHINO Tomotoshi Kobe University, Physics Department, Assoc. Professor, 理学部, 助教授 (00241563)
SAKAMOTO Makoto Kobe University, Physics Department, Assistant Professor, 理学部, 助手 (30183817)
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| Project Period (FY) |
2002 – 2005
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| Keywords | exact renormalization group / density matrix renormalization group / gauge theories / tensor product variational method |
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| Research Abstract |
We have applied renormalization group (RG) techniques to both quantum field theory and statistical physics. The research in quantum field theory was led by Sonoda, and that in statistical physics by Nishino.
In the applications to quantum field theory, the following results have been obtained:
1. Parametrization of the solutions to the exact RG equations was introduced by examining the behavior of the solutions at a large momentum cutoff
2. The exact RG equation has been reformulated as an integral equation, which gives a formal perturbative solution.
3. The parametrization described in 1 has been applied to QED. The Ward identities constrain the parameters.
In the applications to statistical physics, the following results have been obtained:
1. Avery fast numerical method of the product wave function RG has been developed.
2. Generalizing the matrix products to tensor products, we have formulated the tensor product RG variational method, which can be considered as an extension of the density matrix RG method to higher dimensional systems.
3. Extending the density matrix RG method, we have obtained the stochastic light-cone density matrix RG and the method of snapshot generation. These have been applied to statistical systems, resulting in phase diagrams of 2-and 3-dimensional ANNNI models, and the symmetric 16-vertex model.
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