Kenzo Ishikawa

The Glueball Mass Spectrum in {QCD}: First Results of a Lattice Monte Carlo Calculation

Abstract We perform a variational calculation of the masses of glueballs of various spins and parities in SU(2) gauge theory. The quantum vacuum we use is generated by the lattice Monte Carlo technique. Our first results, obtained on medium sized lattices give m(0+) = (3.6 ± 0.35) Λmom, m(0− = (6.0 ± 1.0)Λmom, m(2+) = (6.5+1.8−1.1)Λmom, various mass upper bounds and information on glueball wave functions.

Magnetic field induced multi-component QED3 and quantum Hall effect

Dynamics of two dimensional electrons under the strong perpendicular magnetic field is shown to be described by a multi-component fermion theory. The electric conductance has a remarkable property known as the quantum Hall effect. The Hall conductance is quantized in units ofe2/h in the gap region and in the localized state region. The proof of exactness is presented in general cases using quantum field theory.

A Microscopic Theory of the Quantum Hall Effect

Abstract A general proof of the integer quantization of the static Hall conductivity based on the Ward-Takahashi identity is given. The Ward-Takahasi identity is so general that electron-impurity and electron-electron interactions can be incorporated. Finite temperature and finite size effects are also studied and the experimental characteristics are shown to be reproduced. The value on the plateau agrees with an integer multiple of e 2 /2π h .

On the Topological Structure of the Vacuum in SU(2) and SU(3) Lattice Gauge Theories

Abstract We present Monte Carlo measurements of the net topological charge of the vacuum in SU(2) and SU(3) lattice gauge theories. In both cases there is no evidence of any topological structure, and the values obtained are a factor of O(100) smaller than expectations based on analyses of the U(1) problem. Moreover we find a strong sensitivity to the lattice size and to the boundary conditions imposed on the lattice. We comment on the physical significance of these results, establish criteria for the reliable performance of such calculations, and remark on the possibly detrimental impact of these findings on the calculation of hadron spectra.

SU(3) LATTICE MONTE CARLO CALCULATION OF THE GLUEBALL MASS SPECTRUM

Abstract We have calculated the glueball masses of various spins and parities in SU(3) gauge theory. Our first results give m M (0 ++ )=(3.6±0.2) Λ mom , m E (0 ++ )=(4.3±0.3) Λ mom , m (0 −+ )=(7.2 −0.9 +1.6 ) Λ mom , m M (2 ++ )=(8.1±1.1) Λ mom and m E (2 ++ )=(8.3 −1.0 +1.6 ) Λ mom as well as information on the glueball wave functions.

Stochastic quantization of supersymmetric field theory

Abstract The Parisi-Wu stochastic quantization method is applied to supersymmetric field theory. The Langevin equation, which reproduces the Green functions of euclidean field theory, is written in terms of superfields. Supersymmetric U(1) theory under gauge fixing and the large N reduction in chiral SU( N ) theory are discussed. Regularization based on the stochastic method is studied also.

Calculation of the Glueball Mass Spectrum of SU(2) and SU(3) Nonabelian Lattice Gauge Theories. 2. SU(3)

We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0++, 2++, 0−+ and, most interestingly from the experimental point of view, the oddball 1−+. We calculate the 0++ and 2++ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature.

Calculation of the glueball mass spectrum ofSU (2) andSU (3) non-abelian lattice gauge theories I: Introduction andSU (2)

We describe a direct method for calculating the glueball mass spectrum in QCD and apply it to theSU (2) non-abelian gauge theory. The method involves the applicatio of Monte Carlo methods to the lattice regulated theory. We calculate the masses of states of various spins and parity. We check for the absence of finite size effects, for the desired renormalization group dependence and that our higher mass states do not merely reflect a continuum cut. Finally we repeat the calculation in the “Hamiltonian” limit and in the high temperature deconfining phase of QCD.

Prediction of low-lying oddballs in lattice QCD

Abstract We find, in a high precision Monte Carlo calculation of the glueball mass spectrum in pure SU(3) lattice gauge theory, a low-lying oddball with quantum numbers 1 −+ . We estimate its mass to be m (1 −+ )=1.68±0.18 GeV. We also measure the mass of the 0 −− oddball and find m (0 −− )=2.79±0.22 GeV.

DUALITY RELATION AMONG PERIODIC-POTENTIAL PROBLEMS IN THE LOWEST LANDAU LEVEL

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.