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
書誌事項
- タイトル
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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
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大阪大学
- 取得学位
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理学博士
- 学位授与番号
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甲第4424号
- 学位授与年月日
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1992-03-25
注記・抄録
博士論文
目次
- CONTENTS / p3 (0004.jp2)
- ACKNOMLEDGMENT / p5 (0006.jp2)
- §0.INTRODUTION / p1 (0007.jp2)
- §1.REVIEW OF PERTURBATIVE THEORY OF 2D GRAVITY / p6 (0012.jp2)
- 1.1.Critical exponents in the continuum approach to 2D quantum gravity / p6 (0012.jp2)
- 1.2.Lattice formulation of 2D quantum gravity:A scaling behaviour in the matrix models of random surface / p9 (0015.jp2)
- 2.ONE-MATRIX MODEL OF 2D QUANTUM GRAVITY / p14 (0020.jp2)
- 2.1.The method of orthogonal polynomial for one-matrix model / p15 (0021.jp2)
- 2.2.The string equation of the one-matrix model on sphere / p19 (0025.jp2)
- 2.3.The string equation of nonperturbative 2D quantum gravity / p21 (0027.jp2)
- §3.MULTI-MATRIX MODEL OF 2D QUANTUM GRAVITY COUPLED TO CONFORMAL MATTERS / p27 (0033.jp2)
- 3.1.A method of integration over 2-matrices / p27 (0033.jp2)
- 3.2.The method of integration over multi-matrix chain / p33 (0039.jp2)
- §4.ORTHONORMAL POLYNOMIAL AND INTEGRABLE SYSTEMS FOR MATRIX MODEL / p37 (0043.jp2)
- 4.1.The lattice hierarchy of matrix models / p37 (0043.jp2)
- 4.2.Continuum limit of the lattice integrable system formulations / p41 (0047.jp2)
- §5.MAPPING BETWEEN MATRIX MODEL AND KDV HIERARCHY / p48 (0054.jp2)
- 5.1.Two examples of the matrix models / p58 (0054.jp2)
- 5.2.Gravitional dressed scaling operators in terms of Lax operators / p53 (0059.jp2)
- §6.SCHWINGER-DYSON LOOP EQUATION APPROACH TO 2D GRAVITY / p57 (0063.jp2)
- §7.KP HIERARCHY AND 2D GRAVITY / p74 (0080.jp2)
- 7.1.1.Lax representation of generalized KdV hierarchy / p74 (0080.jp2)
- 7.1.2.Commuting flows of Lax equations / p76 (0082.jp2)
- 7.1.3.Conservation laws for Lax equations / p76 (0082.jp2)
- 7.1.4.Hamiltonian formalism for Lax equations / p78 (0084.jp2)
- 7.1.5.Generalized KdV equations and the formal Baker function / p79 (0085.jp2)
- 7.1.6.KP hierarchy and the Baker function / p80 (0086.jp2)
- 7.1.7.The Baker function and the r-function of KP hierarchy / p82 (0088.jp2)
- 7.2.GEL'FAND-DIKII ALGEBRAS AND W-SYMMETRY IN THE MATRIX MODELS / p84 (0090.jp2)
- §8.LOOP EQUATION AND VIRASORO CONSTRAINTS IN NON-PERTURBATIVE 2D QUANTUM GRAVITY / p93 (0099.jp2)
- 8.1.Definition of the deformation operator of Virasoro algebra constraints / p94 (0100.jp2)
- 8.2.The deformation operator P₍₃₎ for two-matrix model / p99 (0105.jp2)
- 8.3.The deformation operator P₍₄₎ for three-matrix model / p102 (0108.jp2)
- 8.4.L₋₁⊤=0 as the string equation of matrix model / p105 (0111.jp2)
- 8.5.Continuum loop equation for the one-matrix model / p108 (0114.jp2)
- 8.6.Multi-matrix models and W-algebraic constraints / p110 (0116.jp2)
- §9.CONCLUSIONS AND FURTHER REMARKS / p114 (0120.jp2)
- APPENDIX A / p117 (0123.jp2)
- APPENDIX B / p118 (0124.jp2)
- REFERENCES / p120 (0126.jp2)
- FIGURE CAPTIONS / p124 (0130.jp2)
