Topological aspects of classical and quantum (2+1)-dimensional gravity 古典及び量子(2+1)次元重力の位相的側面
この論文にアクセスする
この論文をさがす
著者
書誌事項
- タイトル
-
Topological aspects of classical and quantum (2+1)-dimensional gravity
- タイトル別名
-
古典及び量子(2+1)次元重力の位相的側面
- 著者名
-
早田, 次郎, 1963-
- 著者別名
-
ソウダ, ジロウ
- 学位授与大学
-
広島大学
- 取得学位
-
理学博士
- 学位授与番号
-
甲第831号
- 学位授与年月日
-
1990-03-26
注記・抄録
博士論文
In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g = 0 and g = 1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g = 1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace naoclel of (2+1)-dimensional gravity with the matter fields in the case of g = 0 and y = 1. For g = 0, a wormhole solution is found but for g = 1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g = 1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity.
ABSTRACT / p3 CONTENTS / p4 1 Introduction / p5 2 ADM Canonical Formalism / p9 3 York's Formalism / p13 4 Evolution of the Geometry / p17 5 Phase Space Reduction / p23 6 Linearized Gravity / p27 7 Mini-superspace / p31 8 Quantum Gravity / p35 9 Conclusion / p44 Appendix A / p46 Appendix B / p48 Appendix C / p54
目次
- ABSTRACT / p3 (0005.jp2)
- CONTENTS / p4 (0006.jp2)
- 1 Introduction / p5 (0006.jp2)
- 2 ADM Canonical Formalism / p9 (0008.jp2)
- 3 York's Formalism / p13 (0010.jp2)
- 4 Evolution of the Geometry / p17 (0012.jp2)
- 5 Phase Space Reduction / p23 (0015.jp2)
- 6 Linearized Gravity / p27 (0017.jp2)
- 7 Mini-superspace / p31 (0019.jp2)
- 8 Quantum Gravity / p35 (0021.jp2)
- 9 Conclusion / p44 (0026.jp2)
- Appendix A / p46 (0027.jp2)
- Appendix B / p48 (0028.jp2)
- Appendix C / p54 (0031.jp2)
- COMMENT ON THE NON-RENORMALIZATION THEOREM IN THE FOUR-DIMENSIONAL SUPERSTRINGS / p73 (0036.jp2)
- Reducing the Huge Symmetry Occurring in the Compactification of a String / p1016 (0040.jp2)
- Kac Formulas for G/H Conformal Field Theories / p941 (0044.jp2)
- RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS / p1797 (0048.jp2)
- ABELIAN GAUGE THEORY IN TOPOLOGICALLY NON-TRIVIAL SPACE / p2539 (0054.jp2)
- Linearized Analysis of (2+1)-dimensional Einstein-Maxwell Theory / (0060.jp2)
- Teichmüller Motion of (2+1)-Dimensional Gravity with the Cosmological Constant / (0068.jp2)