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Solvable System with non-trivial Boundary Conditions : Quantum Group and Excahnge Algebra

Research Project

Project/Area Number 06640395
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 素粒子・核・宇宙線
Research InstitutionKYOTO 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 Period (FY) 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)
Keywordsintegrable field theory / boundary conditon / Toda field theory / stability / non-hermiticity / quantum algebra / quantum optics / ceherent state / 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 non-trivial 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 half-space non-linear sigma models was addressed and it was shown the infinite set of non-local 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.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (33 results)

All Other

All Publications (33 results)

  • [Publications] E. Crrigan, P. E. Dorey, R. H. Rietdijik, R. Sasaki: "Affine Toda field theory on a half line" Physics Letters B. 333. 83-91 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A. Fujii and R. Sasaki: "Boundary Effects in Integrable Field Theory on a half line" Progress of Theoretical Physics. 93. 1123-1133 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A. Fujii and R. Sasaki: "Instabilities in Integrable Field Theory on a Half Line" Nonlinear, Dissiptave, Irreversible Quantum Systems. (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S. P. Khastgir and R. Sasaki: "Instability if Solitons in Imaginary coupling affine Toda Field Theory" Progress of Theoretical Physics. 95. 485-501 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S. P. Khastgir and R. Sasaki: "Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories" Progress of Theoretical Physics. 95. 503-518 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M. F. Mourad and R. Sasaki: "Non-linear Sigma Models on a Half Plane" International Journal of modern Physics A. 11. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H. -C. Fu and R. Sasaki: "Exponential and Languerre Squeezed States for su(1,1) Algebra and Calogero-Southerland Model" Physical Review A. 53. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H. -C. Fu and R. Sasaki: "Generally Deformed Oscillator, Isospectral Oscillator System and Hermitian Phase Operatr" Journal Physics A. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Inami and R. Sasaki: "Quantum Field Theory, Integrable Models and Beyond Supplement of Prog. Theor. Phys. 118" 理論物理学刊行会, 389 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 佐々木隆: "物理数学(物理学基礎シリーズ11)" 培風館, 340 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] E.Corrigan, P.E.Dorey, R.H.Rietdijk and R.Sasaki: "Affine Toda field theory on a half line" Physics Letters. B333. 83-91 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A.Fujii and R.Sasaki: "Boundary Effects in Integrable Field Theory on a half line" Progress of Theoretical Physics. 93. 1123-1133 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] A.Fujii and R.Sasaki: "Instabilities in Integrable Field Thory on a Half Line" Nonlinear, Dissipative, Irreversible Quantum Systems. (in press). (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.P.Khastgir and R.Sasaki: "Instability of Solitons in imaginary coupling affine Toda Field Theory" Progress of Theoretical Physics. 95. 485-501 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.P.Khastgir and R.Sasaki: "Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories" Progress of Theoretical Physics. 95. 503-518 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.F.Mourad and R.Sasaki: "Non-linear Sigma Models on a Half Plane" International Journal of modern Phy. A 11 (in press.). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.-C.Fu and R.Sasaki: "Exponential and Laguerre Squeezed States for su(1,1) Algebra and Calogero-Sutherland Model" Physical Review. A53 (in press.). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.-C.Fu and R.Sasaki: "Generally Deformed Oscillator, Isospectral Oscillator System and Hermitian Phase Operator" Journal of Physics. A (submitt). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Inami and R.Sasaki: Quantum Field Theory, Integrable Models and Beyond. Publisher Publication Office, Progress of Theoretical Physics Supplement of Prog.Theor.Phys., 389 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Ryu Sasaki: Mathematics for Physicists (Foundation of Physics 11). Publisher Baihuukan, 340 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] E. Corrigan, P. E. Dorey, R. H. Rietdjik, R. Sasaki: "Affine Toda field theory on a half line" Physics Letters B. 333. 83-91 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] A. Fujii and R. Sasaki: "Boundary Effects in Integrable Field Theory on a half line" Progress of Theoretical Physcis. 93. 1123-1133 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] A. Fujii and R. Sasaki: "Instabilities in Integrable Field Theory on a Half Line" Nonlinear, Dissipative, Irreversible Quantum Systems. (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] S. P. Khastgir and R. Sasaki: "Instability of Solitons in imaginary coupling affine Toda Field Theory" Progress of Theoretical Physics. 95. 483-501 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] S. P. Khastgir and R. Sasaki: "Non-canonical folding of Dynkin diagrams and reduction of affine Toda Theories" Progress of Theoretical Physics. 95. 503-518 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] M. F. Mourad and R. Sasaki: "Non-linear Sigma Models on a Half Plane" International Journal of modern Physcis A. 11. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] H. -C. Fu and R. Sasaki: "Exponential and Languerre Squeezed States for su(1,1) Algebra and Calogero-Sutherland Model" Physical Review A. 53. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] T. Inami and R. Sasaki: "Quantum Field Theory, Integrable Models and Beyond Supplement of Prog. Theor. Phys. 118" 理論物理学刊行会, 389 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 佐々木隆: "物理数学(物理学基礎シリーズ11)" 培風館, 340 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] R.Sasaki: "Reflection Bootstrap Equations for Toda Field Theory" Interface between Physics and Mathematics. 201-212 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] E.Corrigan: "Affine Toda Field Theory on a Half Line" Physics Letters B. 333. 83-91 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] A.Fujii: "Boundary Efects in Intergrable Field Theory on a Half Line" Nonlinear,Dissipative,Irreversible Quantum Systems. (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 佐々木隆: "物理数学" 培風館, 300 (1995)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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