New methods for analyzing quantum field theories
| Project/Area Number |
04640286
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
核・宇宙線・素粒子
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| Research Institution | National Institution for High Energy Physics(KEK) (1993)
The University of Tokyo (1992) |
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Principal Investigator |
KAWAI Hikaru National Institution for High Energy Physics(KEK), Physics Dept, professor, 物理研究部, 教授 (80211176)
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| Project Period (FY) |
1992 – 1993
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| Project Status |
Completed (Fiscal Year 1993)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1993: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1992: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | quantum gravity / string theory / epsilon - expansion / renormalization group / R^2 - gravity / transfer matrix / fractal / nonperturbative effect / ノンクリティカル・ストリング / ストリングの場 / R^2ラグランジアン / 2+ε次元量子重力 / 時空のフラクタル構造 / トランスファーマトリックス / Eー展開 / superstringの非摂動効果 / 場の理論 / 重力場の構成的定義 |
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| Research Abstract |
We developed and applied several new methods for analyzing quantum field theories. In particular, we considered quantum gravity and string theories, and constructed useful nonperturbative frameworks for investigating those systems. First of all, we developed and epsilon - expansion scheme for 2+ epsilon dimensional quantum gravity. Using this scheme, we studied scaling properties of higher dimensional quantum gravity. We next considered R^2 Lagrangian can be solved exactly both in the infrared and ultraviolet limits. Furtheremore, we invented a transfer metrix formalism that can be applied in the presence of quantum fluctuations of the space-time. Using this method, we exactly solved the problem of two-dimensional quantum gravity, and proved that the space-time has fractal structures. This method may be a powerful tool for analyzing nonperturbative effects of string theories. Some attempts in this direction are now in progress.
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Report
(3 results)
Research Products
(18 results)
