Quantum Field Theories in Low Dimensions and Their Application
Grant-in-Aid for Overseas Scientific Survey.
|Allocation Type||Single-year Grants |
|Research Institution||Kyoto University |
INAMI Takeo Yukawa Inst., Kyoto Univ., 基礎物理学研究所, 助教授 (20012487)
PARK QーHan 慶煕大学, 物理学科, 助教授
SOH Kwang Su ソウル国立大学, 教養部, 教授
NAM Soonkeon 慶煕大学, 物理学科, 助教授
CHUNG Bok Ke 慶煕, 物理学科, 教授
YAMADA Yasuhiko Math.Dept., Kyushu Univ., 理学部, 助教授 (00202383)
ODAKE Satoru College of General Education, Shinshu Univ., 教養部, 講師 (40252051)
ISHIBASHI Nobuyuki National Lab.for High Energy Phys.(KEK), 助教授 (70211729)
梁 成吉 筑波大学, 物理学系, 教授 (70201118)
DEGUCHI Tetsuo Phys.Dept., Ochanomizu Univ., 理学部, 助教授 (70227544)
FUJIKAWA Kazuo Phys.Dept., Tokyo Univ., 理学部, 教授 (30013436)
MATSUO Yutaka Yukawa Inst., Kyoto Univ., 基礎物理学研究所, 助教授 (50202320)
SASAKI Ryu Yukawa Inst., Kyoto Univ., 基礎物理学研究所, 助教授 (20154007)
YANG Sung-kil Phys.Dept., Tsukuba Univ.
|Project Period (FY)
Completed (Fiscal Year 1994)
|Keywords||Low dimensional field theory / Integrable field theory / solvafle lattice model / Models with boundaries / 2-dimension al quantum gravity / Walgebras / W代数 / アノマリー|
Many of the important physical phenomena and the methods to deal with them in particle physics and condensed matter physics are of nonperturbative nature and are difficult to solve. The same type of problems appears in physical systems in low dimensions. They are more easily accessible to rigorous methods.
We intended to develop physical and mathematical methods in quantum field theories in low dimensions and to pursue their applications. Specifically we planed to investigate the following problems :
1) Construction of solvable lattice models/integrable field theories with boundaries and their application to condensed matter physics.
2) Construction of other new types of integrable field theories.
3) Non-perturbative methods for 2-dimensional quantum gravity.
4) Topological gravity.
5) Representation theories of W_* and W_N algebras and their application to condensed matter physics.
6) Application of the knot theory to statistical mechanics.
7) Nonperturbative methods in QCD and nonlinear sigm
a model in low dimensions.
8) Application of supersymmetry and anomalies to physics.
We have made progress in the research of most of the problems written above. We give below only a few of them.
Problems 1) We have constructed a few kinds of solvable lattice models and integrable field theories [8,17 of the references] and studied the stability problems in systems on a half line . The Korean team (Nam and his collaborators) has a common interest with lnami and Sasaki on these problems and they have exchnged ideas. As an applicatication of the boundary CFT condensed matter physics, finite-size scaling spectrum in the Kondo problem has been derived .
Problems 5) : Progress has been made in the representation theoretic studies of W_* algebras [11-14], The Calogero-Sutherland type models has been studied from a representation theoretic viepoint of W_N algebras [15,16,19]. Nam has joined the discussion of the Japanese team (Odake, Matsuo).
Problem 7) : This problem has been pursued mainly by the Korean team (Park and his collaborators) ; Inami has joined the discussion . Less
Report (1 results)
Research Products (50 results)