The matrix model of two dimensional quantum gravity and integrable systems 二次元量子重力の行列模型と可積分系

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著者

    • 曽, 一新 チン, イシン

書誌事項

タイトル

The matrix model of two dimensional quantum gravity and integrable systems

タイトル別名

二次元量子重力の行列模型と可積分系

著者名

曽, 一新

著者別名

チン, イシン

学位授与大学

大阪大学

取得学位

理学博士

学位授与番号

甲第4424号

学位授与年月日

1992-03-25

注記・抄録

博士論文

10117

博士(理学)

1992-03-25

大阪大学

14401甲第04424号

目次

  1. CONTENTS / p3 (0004.jp2)
  2. ACKNOMLEDGMENT / p5 (0006.jp2)
  3. §0.INTRODUTION / p1 (0007.jp2)
  4. §1.REVIEW OF PERTURBATIVE THEORY OF 2D GRAVITY / p6 (0012.jp2)
  5. 1.1.Critical exponents in the continuum approach to 2D quantum gravity / p6 (0012.jp2)
  6. 1.2.Lattice formulation of 2D quantum gravity:A scaling behaviour in the matrix models of random surface / p9 (0015.jp2)
  7. 2.ONE-MATRIX MODEL OF 2D QUANTUM GRAVITY / p14 (0020.jp2)
  8. 2.1.The method of orthogonal polynomial for one-matrix model / p15 (0021.jp2)
  9. 2.2.The string equation of the one-matrix model on sphere / p19 (0025.jp2)
  10. 2.3.The string equation of nonperturbative 2D quantum gravity / p21 (0027.jp2)
  11. §3.MULTI-MATRIX MODEL OF 2D QUANTUM GRAVITY COUPLED TO CONFORMAL MATTERS / p27 (0033.jp2)
  12. 3.1.A method of integration over 2-matrices / p27 (0033.jp2)
  13. 3.2.The method of integration over multi-matrix chain / p33 (0039.jp2)
  14. §4.ORTHONORMAL POLYNOMIAL AND INTEGRABLE SYSTEMS FOR MATRIX MODEL / p37 (0043.jp2)
  15. 4.1.The lattice hierarchy of matrix models / p37 (0043.jp2)
  16. 4.2.Continuum limit of the lattice integrable system formulations / p41 (0047.jp2)
  17. §5.MAPPING BETWEEN MATRIX MODEL AND KDV HIERARCHY / p48 (0054.jp2)
  18. 5.1.Two examples of the matrix models / p58 (0054.jp2)
  19. 5.2.Gravitional dressed scaling operators in terms of Lax operators / p53 (0059.jp2)
  20. §6.SCHWINGER-DYSON LOOP EQUATION APPROACH TO 2D GRAVITY / p57 (0063.jp2)
  21. §7.KP HIERARCHY AND 2D GRAVITY / p74 (0080.jp2)
  22. 7.1.1.Lax representation of generalized KdV hierarchy / p74 (0080.jp2)
  23. 7.1.2.Commuting flows of Lax equations / p76 (0082.jp2)
  24. 7.1.3.Conservation laws for Lax equations / p76 (0082.jp2)
  25. 7.1.4.Hamiltonian formalism for Lax equations / p78 (0084.jp2)
  26. 7.1.5.Generalized KdV equations and the formal Baker function / p79 (0085.jp2)
  27. 7.1.6.KP hierarchy and the Baker function / p80 (0086.jp2)
  28. 7.1.7.The Baker function and the r-function of KP hierarchy / p82 (0088.jp2)
  29. 7.2.GEL'FAND-DIKII ALGEBRAS AND W-SYMMETRY IN THE MATRIX MODELS / p84 (0090.jp2)
  30. §8.LOOP EQUATION AND VIRASORO CONSTRAINTS IN NON-PERTURBATIVE 2D QUANTUM GRAVITY / p93 (0099.jp2)
  31. 8.1.Definition of the deformation operator of Virasoro algebra constraints / p94 (0100.jp2)
  32. 8.2.The deformation operator P₍₃₎ for two-matrix model / p99 (0105.jp2)
  33. 8.3.The deformation operator P₍₄₎ for three-matrix model / p102 (0108.jp2)
  34. 8.4.L₋₁⊤=0 as the string equation of matrix model / p105 (0111.jp2)
  35. 8.5.Continuum loop equation for the one-matrix model / p108 (0114.jp2)
  36. 8.6.Multi-matrix models and W-algebraic constraints / p110 (0116.jp2)
  37. §9.CONCLUSIONS AND FURTHER REMARKS / p114 (0120.jp2)
  38. APPENDIX A / p117 (0123.jp2)
  39. APPENDIX B / p118 (0124.jp2)
  40. REFERENCES / p120 (0126.jp2)
  41. FIGURE CAPTIONS / p124 (0130.jp2)
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各種コード

  • NII論文ID(NAID)
    500000084246
  • NII著者ID(NRID)
    • 8000000084457
  • DOI(NDL)
  • NDL書誌ID
    • 000000248560
  • データ提供元
    • 機関リポジトリ
    • NDL-OPAC
    • NDLデジタルコレクション
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