2006 Fiscal Year Final Research Report Summary
Development and Application of Non-Perturbative Method to Analyze Gauge Field Theories
| Project/Area Number |
13135211
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Kanazawa University |
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Principal Investigator |
AOKI Ken-Ichi Kanazawa University, Graduate School of Natural Science and Technology, Professor (00150912)
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| Co-Investigator(Kenkyū-buntansha) |
HIRAYAMA Minoru Toyama University, Graduate School of Natural Science and Engineering, Professor (80018986)
TERAO Haruhiko Kanazawa University, Graduate School of Natural Science and Technology, Associate Professor (40192653)
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| Project Period (FY) |
2001 – 2006
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| Keywords | non-perturbative method / gauge theory / renormalization group / spontaneous symmetry breaking / soliton / skyrmion / hierarchy problem / higgs particle |
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| Research Abstract |
K-I. A studied the non-perturbative renormalization group method to investigate the dynamical chiral symmetry breaking in gauge theories. The mean field method so far like the Schwinger-Dyson equation suffers a serious gauge dependence. The non-perturbative renormalization group beta functions can be improved to give less gauge dependent physical results by taking account of non-ladder type diagrams. The chiral phase structures in the hot and dense QCD matter is a hot topic in the high energy physics and nuclear physics, and the non-perturbative renormalization group beta function in the hot and dense states are evaluated and the importance of the effective potential and the Lorentz non-invariant operators are found. Also, the infinite range interactions are studied with the simplest Ising model. Introducing a new method of finite range scaling, we evaluate the critical coupling constant and the exponent by referring to the zeta function.
M. H investigated Skyrme model and Fadeev model
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and got various new results about the exact solutions and energy eigen values. Fadeev model with a weight function for the kinetic term or interaction terms is proved to be solved exactly. Two parameter exact solutions for Skyrme model are found, which depends on the interaction constant and have vanishing Baryon number. Three parameter exact solution for Skyrme model are given by elliptic functions and they have non-vanishing Baryon number. As a special case for this class of solutions, we confirm a domain wall solution numerically. In SU (2) gauge theory, the Fadeev-Niemi field for the Melon configuration is interpreted as a monopole-antimonopole pair. We tried a new profile function for Skyrmion and got lower energy eigen values.
H, T, studied mainly origin of large hierarchy in the parameters of the standard model of elementary particles as well as the supersymmetric models from dynamical point of view. Especially he considered the renormalization properties of field theories possessing infrared fixed points and studied role of large anomalous dimensions to realize hierarchical parameters in various models. Explicitly, he considered various models leading to the hierarchy in masses of elementary particles, universal masses of the superparticles in supersymmetric extensions so as not to generate the flavor changing neutral currents, and the mass hierarchy of the Higgs particle in the standard model as well as the supersymmetric extension. The dynamical properties of the models were analyzed by means of non-perturbative renormalization group. H. T also developed the analysis of renormalization group analysis of (supersymmetric) gauge theories with infrared fixed points simultaneously. Less
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