Nonperturbative solutions for canonical quantum gravity 正準量子重力における非摂動論的解
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Author
Bibliographic Information
- Title
-
Nonperturbative solutions for canonical quantum gravity
- Other Title
-
正準量子重力における非摂動論的解
- Author
-
江澤, 潔
- Author(Another name)
-
エザワ, キヨシ
- University
-
大阪大学
- Types of degree
-
博士 (理学)
- Grant ID
-
甲第5412号
- Degree year
-
1996-03-25
Note and Description
博士論文
Table of Contents
- Abstract / p1 (0002.jp2)
- Contents / p2 (0003.jp2)
- 1 Introduction / p3 (0004.jp2)
- 1.1 Motivations for quantum gravity / p3 (0004.jp2)
- 1.2 Issues on canonical quantum gravity / p5 (0006.jp2)
- 1.3 Ashtekar's formalism and solutions to the Wheeler-De Witt equation / p6 (0007.jp2)
- 1.4 An outline of this paper / p6 (0007.jp2)
- 2 Ashtekar's formalism / p8 (0009.jp2)
- 2.1 Classical theory / p8 (0009.jp2)
- 2.2 Quantization / p14 (0015.jp2)
- 3 Spin network states / p16 (0017.jp2)
- 3.1 Backgrounds and the definition / p16 (0017.jp2)
- 3.2 The induced Haar measure on SU(2) gauge theories / p19 (0020.jp2)
- 3.3 The coherent state transform and the induced heat-kernel measure / p23 (0024.jp2)
- 3.4 The Wick rotation transform / p25 (0026.jp2)
- 3.5 Diffeomorphism invariant states / p26 (0027.jp2)
- 3.6 Area and volume operators / p28 (0029.jp2)
- 3.7 Spin network states in terms of spinor propagators / p29 (0030.jp2)
- 4 Combinatorial solutions to the Wheeler-De Witt equation / p31 (0032.jp2)
- 4.1 Action of the scalar constraint on spin network states / p32 (0033.jp2)
- 4.2 Topological solutions / p36 (0037.jp2)
- 4.3 Analytic loop solutions / p37 (0038.jp2)
- 4.4 Combinatorial solutions / p37 (0038.jp2)
- 4.5 Issues on the combinatorial solutions / p40 (0041.jp2)
- 5 Discretized Ashtekar's formalism / p42 (0043.jp2)
- 5.1 Multi-plaquette solutions / p44 (0045.jp2)
- 5.2 Lessons to the continuum theory / p46 (0047.jp2)
- 6 Topological solutions / p47 (0048.jp2)
- 6.1 SL(2,C) BF theory and topological solutions / p47 (0048.jp2)
- 6.2 WKB orbits of the Chern-Simons solutions / p49 (0050.jp2)
- 6.3 Semiclassical interpretation of Ψtopo〔A〕 / p51 (0052.jp2)
- 6.4 The case of M⁽³⁾≈T³ / p55 (0056.jp2)
- 6.5 The Euclidean case / p59 (0060.jp2)
- 6.6 Topological solutions for N=1 supergravity / p60 (0061.jp2)
- 6.7 Summary and discussion on §6 / p64 (0065.jp2)
- 7 Other solutions and remaining issues / p64 (0065.jp2)
- 7.1 Loop representation and the Jones polynomial / p65 (0066.jp2)
- 7.2 The wormhole solution in N=1 supergravity / p66 (0067.jp2)
- 7.3 Remaining issues / p67 (0068.jp2)
- Appendix A The projector [数式] / p70 (0071.jp2)
- Appendix B Invariant measures on SU(2) and SL(2,C) / p70 (0071.jp2)
- B.4 The Haar measure on SU(2) / p71 (0072.jp2)
- B.5 The heat-kernel measure on SL(2,C) / p71 (0072.jp2)
- Appendix C Basic action of the renormalised scalar constraint / p73 (0074.jp2)
