2006 Fiscal Year Final Research Report Summary
Quantization of Space-Time and Gravitational Field
| Project/Area Number |
15540261
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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 Graduate University for Advanced Studies |
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Principal Investigator |
YUKAWA T. The Graduate University for Advanced Studies, Hayama Center for Advanced Studies, Professor, 葉山高等研究センター, 教授 (20110091)
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| Project Period (FY) |
2003 – 2006
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| Keywords | Quantum gravity / Simplicial quantum gravity / Random matrix theory / Boundary Liouville theory / Cosmic microwave background / Fluctuation anisotropy / Origin of universe / Dynamical triangulation |
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| Research Abstract |
Study of quantum gravity has two major purposes, firstly quantizing graviton to achieve a renormalizable quantum field theory of gravity, and secondly the quantum cosmology to create space-time. For the first topics we employ a numerical method known as the dynamical triangulation of the simplicial gravity to perform quantization of the Einstein general relativity, non-perturbatively. As for the second subject the dynamical triangulation is extended to create d-dimensional (d=2,3, and 4) manifold with the open topology of disk.
Time is defined proper to the topology through the relation between the d-dimensional disk volume and the (d-1)-dimensional boundary surface area. Space coordinate system is embedded on the d-sphere with the distance defined through geodesic distance. In order to check the correctness of algorithm analytical solutions of the boundary Liouville field theory and the matrix models in 2-dimension are utilized.
The method is applied to analyze the anisotropies of the cosmic microwave background by measuring the 2-point scalar curvature correlation on the last scattering surface created in the d-dimensional disk. It shows qualitative agreement to the 2-point temperature correlation observed by the WRAP mission.
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