| Project/Area Number |
17540242
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Ehime University (2006-2007)
Niigata University (2005) |
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Principal Investigator |
SO Hiroto Ehime University, Graduate School of Science and Engineering, Professor (20196992)
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| Co-Investigator(Kenkyū-buntansha) |
IGARASHI Yuji Niigata University, Institute of Humanities, Social Sciences and Education, Professor (50151262)
ITOH Katsumi Niigata University, Institute of Humanities, Social Sciences and Education, Associate Professor (50242392)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,410,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | lattice field theory / supersymmetry / Majorana fermion / master equation / 素粒子論 / 場の理論 / 格子ゲージ理論 / 超対称性 / 繰り込み群 / 格子理論 / 市松模様格子 |
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| Research Abstract |
The purpose of this project is to construct regularized field theories in order to understand a unified (supersymmetric) mode of fundamental particle physics and to obtain a new idea on symmetry realized in regularized field theories.
Since our fundamental particle physics is dominated by “gauge principle", its regularized version must be also gauged. The lattice gauge theory is a most suitable approach but the usual cubic lattice is less symmetry than our world.
An Ichimatsu-patterned lattice has a substructure inside the normal cubic lattice. It is characteristic on account of fermionic degrees of freedom. We have made it clear that fermi fields on a Ichimatsu-patterned lattice are described by SO(2D) not SO(D) where D is space-time dimension. This surprising fact leads us to understand a doubling phenomena that fermionic degrees are 2^<(2D)/2> not 2^<D/2> in a unit lattice. Supersymmetric theories have a balance between bosonic and fermionic degree of freedom, and the counterpart for gauge freedom remains as an open problem.
Why is the realization of supersymmetry difficult unlike gauge symmetry? One of reasons is the path integral measure of fermi fields. The simplest case is a 0-dimensional case and we have studied the global anomaly under the existence of Majorana fermions. The consequence is that the consistent theory enforces us even number of Majorana fermions in the theory such as Witten's anomaly. On the other hand, how can we set a Majorana fermion on lattice? According to an approach of Luescher for a chiral symmetry, we have tried a Majorana condition. To our regret, the result is not satisfied with chiral Yukawa couplings. Therefore, we need to get systematical approach of symmetry in regularized filed theories. The quantum master equation can describe the realization necessarily and sufficiently. This approach can apply to a system with external gravitational fields.
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