| Project/Area Number |
17540234
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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 | The University of Tokyo |
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Principal Investigator |
NISHIJIMA Kazuhiko The University of Tokyo, Graduate School of Science, Emeritus Professor (50011424)
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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 |
¥1,950,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | quark / gluon / confinement / color / gauge parameter / non-commutative geometry / quantum shift / non-commutative field / ゲージ場理論 / ゲージ・パラメター / 同値ゲージ類 / くりこみ群 / QCD / QED / 非可換座標 / 非可換空間座標 / 非可換量子場 / QUANTUM SHIFT / 空間座標のゆらぎ / カラーの閉じ込め / 量子色力学 / ゲージの選び方 / グルーオンの質量 / WEYL-MOYAL積 |
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| Research Abstract |
1. Quark Confinement and the Gluon Mass Quantum chromodynamics (QCD) is the gauge theory of the quark-gluon interaction. A characteristic feature of this system consists in the point that any particle carrying a non-vanishing color quantum number is unobservable, in particular, colored quarks have never been observed to date. This is called quark confinement or more generally color confinement.
The Lagrangian of QCD generally depends on a parameter called the gauge parameter and it is believed that an observable quantity in the gauge theory does not depend on this parameter. We are going to check if this independence is generally true. We show that this independence on the gauge parameter is certainly true in quantum electrodynamics (QED), but it is not in QCD.
In QCD when the gauge parameter is negative the situation is completely different from the case of positive parameter. In the negative case color confinement is realized and the gluon mass turns out to be finite or non-zero. This
… More
is our conclusion.
2. Field Theory in the Non-Commutative Geometry Assume that different components of the space coordinates do not commute because of their quantum fluctuation and construct field theories in this non-commutative geometry. In the present approach we decompose the non-commutative coordinates as the sum of commutative ones and quantum fluctuation called the quantum shift. We start from the commutative quantum field theory(CQFT) and infuse the quantum shift into it in order to realize the non-commutative field theory(NCQFT). Then this operation generates a mapping of a CQFT into the corresponding NCQFT. In this way we study how NCQFT deviates from CQFT, in particular, how the S matrix in NCQFT deviates from Lorentz invariance.
We start from the commutative quantum field theory (CQFT) and infuse the quantum shift into it in order to realize the non-commutative field theory (NCQFT). Then this operation generates a mapping of a CQFT into the corresponding NCQFT. In this way we study how NCQFT deviates from CQFT, in particular, how the S matrix in NCQFT deviates from Lorentz invariance. Less
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