Solvable System with nontrivial Boundary Conditions : Quantum Group and Excahnge Algebra
Project/Area Number  06640395 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
素粒子・核・宇宙線

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
SASAKI Ryu Kyoto University, Yukawa Inst.for Theor. Phys. Associate Professor, 基礎物理学研究所, 助教授 (20154007)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1995 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1994 : ¥500,000 (Direct Cost : ¥500,000)

Keywords  integrable field theory / boundary conditon / Toda field theory / stability / nonhermiticity / quantum algebra / quantum optics / ceherent state / 解ける場の理論 / 量子光学 / 境界条件 / 戸田場の理論 / 安定性 / 非エルミート理論 / 量子代数 / コヒーレント状態 / 可解系 / 非自明な境界条件 / 境界による不安定性 / 反射方程式代数 
Research Abstract 
In this project, we chose "quantum field theory with nontrivial boundary condition" as an interesting and promising generalisation and extension of integrable quantum field theory, solvable lattice models and two dimensional conformal field theory in the whole space, which have been rather well understood. At first, for the general question : given an exactly solvable theory in the whole space, " is it solvable in a half space by imposing appropriate boundary conditions? " we gave a positive answer for general affine Toda field theories. The next question was : "are all the classically integrable field theories on a half space quantum integrable? " We answered that only a very limited part was allowed by the stability. The criterion for stability was applied to the "solitons" in the affine Toda field theory with "pure imaginary coupling constant". Together with the hermiticity we concluded that "quantum corrections to the soliton masses" was not justifiable. The integrability of the halfspace nonlinear sigma models was addressed and it was shown the infinite set of nonlocal charges was not conserved for the free boundary condition in half space, in sharp contrast to the affine Toda case. The reduction of the equation of motion of affine Toda field theory was investigated systematically and comprehensively. Many new reduction relations were found. We investigated relatively simple physical systems with finite degrees of freedom and discussed the effects of the quantum group (algebra), which was another big element of the current research. The representation of the minimum uncertainty states in quantum optics, like the coherent and the squeezed states were given in terms of various quantum algebras. 量子群、交換代数等の力学的影響を理解する一助として比較的構造の簡単な自由度の物理系を扱った。特に量子光学で重要な役割を果たす不確定性が最小となるCoherent状態やSqueezed状態に関連して多くの量子代数(一般化された変形振動子代数、q変形振動子、アイソスペクトラル振動子、CalogeroSutheriand系等)とその表現を与えた。

Report
(4results)
Research Output
(33results)