Grant-in-Aid for Scientific Research (B).
|Allocation Type||Single-year Grants|
|Research Institution||HOKKAIDO UNIVERSITY|
ISHIKAWA Kenzo Hokkaido Univ., Grad. School of Science, Prof., 大学院・理学研究科, 教授 (90159690)
SUZUKI Hisao Hokkaido Univ., Grad. School of Science, Asso. Prof., 大学院・理学研究科, 助教授 (20192619)
NAKAYAMA Ryuichi Hokkaido Univ., Grad. School of Science, Asso. Prof., 大学院・理学研究科, 助教授 (30217947)
KAWAMOTO Noboru Hokkaido Univ., Grad. School of Science, Prof., 大学院・理学研究科, 教授 (50169778)
SUEHIRO kazuhiko Hokkaido Univ., Grad. School of Science, Lect., 大学院・理学研究科, 講師 (60211976)
JACKIW Roman マサチューセッツ工科大学, 物理学科, 教授
WIEGMANN Pau シカゴ大学, スラランク研究所, 教授
細谷 裕 ミネソタ大学, 物理天文学部, 教授
|Project Period (FY)
1998 – 1999
Completed(Fiscal Year 1999)
|Budget Amount *help
¥6,100,000 (Direct Cost : ¥6,100,000)
Fiscal Year 1999 : ¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1998 : ¥3,300,000 (Direct Cost : ¥3,300,000)
|Keywords||quantum Hall effect / negative pressure / Chern-Simons term / Chern-Simons gravity / lattice gravity / Symmetry od D-Particle / phase transition of superstring / quantum entropy / 量子エントロピー / チャーン・サイモン項 / トポロジカル不変量 / 偶数次元チャーン・サイモン項 / N=2超対称ゲージ理論 / P・T非保存の超伝導・超流動|
In this project, fundamental problems of low dimensional physical systems such as field theory of quantum Hall effects, quantum gravity, super string, and super symmetric gauge theory and others are investigated and the following results have been obtained:
(1)Compressible gas states of quantum Hall system have been established based on Hartree Foch theory on von Neumann lattice. They have anisotropic density moduration, nagative pressure and compressibility. Negative pressure leads quantum Hall effect to have unusual stability. Generalized flux state which connects fractional Hall effect with Hofstadter butterfly was proposed.
(2)Chern-Simons theory was generalized to even dimensions and was quantized as an infinity reducible constrained system consistently.
(3)Time reversal violating superconductors was analyzed and was shown to have pseudo Chern-Simons term in effective action. Experiment for its observation was also proposed.
(4)Chern-Simons gravity and BF gravity were defined on lattice.
(5)Conformal invariance of D-particle was shown and a new formulation based on Hamiltonian-Jacobi method was achieved.
(6)A new technique to compute physical quantities at around critical point where conformal invariance was applied was developed.
(7)Universal inequarities for entanglement entropy in quantum information theory was derived. A universal connection of conformal mapping with Toda heirechies and two-dimensional gravity was established.