Phase Structures of Field Thoeries with Topological Term
Project/Area Number  07640417 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
素粒子・核・宇宙線

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

CoInvestigator(Kenkyūbuntansha) 
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)

Keywords  Lattice 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 betarheta 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. Nontrivial IR fixed point appears at rheta=pi as in the case (i). For rheta*pi, successive RG transformations induce the nonabelian representations in the imaginary part of the action. But these trajectories end up with the IR fixed point at beta=0.

Report
(3results)
Research Output
(14results)