Non-unitary evolution of noncommutative spaces and its application as models of the universe
| Project/Area Number |
16540244
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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 | Kyoto University |
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Principal Investigator |
SASAKURA Naoki Kyoto University, Yukawa Institute for Theoretical Physics, Associate Professor (80301232)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,050,000 (Direct Cost: ¥1,900,000、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: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2004: ¥400,000 (Direct Cost: ¥400,000)
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| Keywords | Tensor model / Rank-three tensor / Fuzzy space / Quantum gravity / General relativity / Spacetime uncertainty relation / Vacuum energy / Dark energy / 非可換空間 / ホップ代数 / Twisted symmetry / Braided field theory / ダイナミカル / 非結合代数 / 非可換幾何学 / 一般座標変換 / 非可換球面 / 宇宙 / 時間発展 / 保存カレント / 幾何 / 熟核 / 漸近展開 |
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| Research Abstract |
Through the recent astrophysical observations, it has become clear that the most part of our universe is composed of the unidentified dark matter and dark energy. Especially the dark energy is a long-standing problem also in elementary particle physics, which is known as the cosmological constant problem or the vacuum energy problem. Probably, the solution requires the development of new quantum theory of gravity, which replaces the general relativity, the classical theory of gravity.
General relativity is based on the concept of Riemannian geometry, and its dynamical variable is the metric tensor, which varies continuously on a coordinated spacetime. It is well known that the standard procedure of field quantization cannot be applied to the general relativity, because of the appearance of uncontrollable divergences. Moreover some thought experiments based on the general relativity and the quantum mechanics suggest the existence of the observable minimum length, and do not seem to favor the classical continuous and smooth spacetime. The concept of fuzzy spaces is an interesting candidate for such quantum spacetimes. In this granted project, I have pursued the possibilities to construct quantum gravity based on dynamical theory of filmy spaces. A fuzzy space can be defined by a rank-three tensor which determines the product rules among functions. Thus I have proposed dynamical theory of a rank-three tensor as that of fuzzy spaces. Such a rank-three tensor model is a background-independent theory which describes dynamical spaces of various topologies and dimensions in a unified manner. I have numerically studied the models, and have found that they can produce various physically meaningful spaces as classical solutions, and reproduces general relativity in the classical limit. Thus the rank-three tensor model provides an interesting candidate for quantum gravity well worth further study.
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Report
(5 results)
Research Products
(30 results)
