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Phase Structures of Field Thoeries with Topological Term

Research Project

Project/Area Number 07640417
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 素粒子・核・宇宙線
Research InstitutionSaga University

Principal Investigator

YONEYAMA Hiroshi  Saga University, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (50210795)

Co-Investigator(Kenkyū-buntansha) IMACHI Masahiro  Yamagata University, Faculty of Science, Professor, 理学部, 教授 (70037208)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1996: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
KeywordsLattice gauge theory / Topological term / Phase Structure / Monte Carlo simulation / Real space renormalization group / Topological charge / Fixed point action / 場の理論 / トポロジー / シ-タ真空 / 相転移 / 実空間くりこみ群
Research Abstract

Phase structures of lattice field theories with topological term are studied by means of (1) Monte Carlo (MC) simulations as well as (2) real space renormalization group (RSRG) method. (1) In MC study, the notorious problem of the complex Boltzmann weights due to the complex action of the topological term is overcome by calculating the topological charge distribution P (Q). The partition function is calculated by fourier transforming P (Q). CP^1 model is studied for two cases ; (i) standard action and (ii) fixed point (EP) action. (i) In the strong coupling regions, P (Q) behaves as gaussian with the exponent proportional to 1/V (V : volume of the system). This turns out to show the first order phase transition at rheta=pi. In the weak coupling regions, the transition disappears. In the beta-rheta plane no other signatures of phase transitions are found. (ii) In the case of the FP action, this 1st order phase transition occurs only at rheta=pi in the strong coupling limit.
(2) RSRG study has applied to (i) U (1) and (ii) U (2) gauge models in two dimensions. Irreducible character expansions are useful in order to obtain the closed form of the RG equation. (i) In U (1) case, the non trivial infrared (IR) fixed point appears besides the IR fixed point at the strong coupling limit. P (Q) is calculated analytically and shows the gaussian behavior. For any value of the coupling constant, the model undergoes the 1st. order phase transition at rheta=pi. This agrees with the results of MC simulations. (ii) In U (2) case, model with the Wilson real action and the standard imaginary action (abelian) is studied. Non-trivial IR fixed point appears at rheta=pi as in the case (i). For rheta*pi, successive RG transformations induce the non-abelian representations in the imaginary part of the action. But these trajectories end up with the IR fixed point at beta=0.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] S.Tominaga: "Chiral Perturbation Theory,Finite Size Effects,and Three Dimensional XY model" Physical Review. B51. 8243-8253 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.S.Hassan: "Character Expansion,Zeroes of Partition Function and θ Term in U(1) Gauge Theory" Progress of Theoretical Physics. 94. 861-871 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.S.Hassan: "Topological Charge Distribution and CP^1 Model with θ Term" Progress of Theoretical Physics. 95. 175-189 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Imachi: "Renormalization Group Analysis of U(2) Gauge Theory with θ-Term in 2 Dimensions" Progress of Theoretical Physics. 97(to appear in No.5). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Tominaga and H.Yoneyama: "Chiral Perturbation Theory, Finite Size Effects, and Three Dimensional XY model" Physical Review. B51, No13. 8243-8253 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.S.Hassan, M.Imachi, N.Tsuzuki and H.Yoneyama: "Character Expansion, Zeroes of Partition Function and rheta-Term in U (1) Gauge Theory" Progress of Theoretical Physics. 94, No5. 861-871 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.S.Hassan, M.Imachi, N.Tsuzuki and H.Yoneyama: "Topological Charge Distribution and CP1 Model with rheta Term" Progress of Theoretical Physics. 95, No1. 175-189 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Imachi, T.Kakitsuka, N.Tszuki and H.Yoneyama: "Renormalization Group Analysis of U (2) Gauge Theory with rheta Term in 2 Dimensions" Progress of Theoretical Physics. 97, No.5. (to appear). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Shin-ichi Tominaga: "Chiral Perturbation Theory,Finite Size Effects,and the Three Dimensional XY Model" Physical Review. B51・13. 8243-8253 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Ahmed S.Hassan: "Character Expansion,Zeroes of Partition Function and θ-Term in U(1) Gauge Theory" Progress of Theoretical Physics. 94・5. 861-871 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Ahmed S.Hassan: "Topological Charge Distribution and CP^1 Model with θ Term" Progress of Theoretical Physics. 95・1. 175-189 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Ahmed S.Hassan: "Real Space Renormalization Group Analysis of U(1)-Gauge Theory with θ Term in 2 Dimensions" Progress of Theoretical Physics. 93. 161-172 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Ahmed S.Hassan: "Character Expansion,Zeroes of Partition Function and θ Term in U(1) Gauge Theory" Progress of Theoretical Physics. 94. 861-871 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Ahmed S.Hassan: "Topological Charge Distribution and CP^1 Model with θ-Term" Progress of Theoretical Physics. 95. 175-189 (1996)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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