arXiv subjects
Publications and source records attributed to Hideo Nakajima.
The colour confinement criterion proposed by Kugo and Ojima is tested in the lattice Landau gauge QCD simulation. The renormalization effects are studied by measuring the gluon propagator, ghost propagator, three gluon vertex and the ghost-antighost-gluon vertex.
The Kugo-Ojima color confinement criterion, which is based on the BRST symmetry of the continuum QCD is numerically tested by the lattice Landau gauge simulation. We first discuss the Gribov copy problem and the BRST symmetry on the lattice. The lattice Landau gauge can be formulated with options of the gauge field definition, U(link)-linear type or log U type. The Kugo-Ojima parameter u^a_b which is expected to be -1^a_b in the continuum theory is found to be -0.7*1^a_b in the strong coupling region, and the magnitude is a little less in the weak coupling region in log U type simulation. Those values are weakened even further in U-linear type. The horizon function defined by Zwanziger is evaluated in both types of gauge field and compared. The horizon function in the log U version is larger than the other, but in the weak coupling region, the expectation value of the horizon function is suggested to be zero or negative.
The Kugo-Ojima color confinement criterion, which is based on the BRST symmetry of QCD is numerically tested by the lattice Landau gauge simulation. We first discuss the BRST symmetry on the lattice and the Gribov copy problem. The horizon function defined by Zwanziger based on the U-linear definition of the gauge field and that based on log U are compared. The parameter u which is expected to be $-1δ^a_b$ in the continuum theory was found to be $-0.7δ^a_b$ in the strong coupling region. There are about 20% difference between the two horizon functions, but in the weak coupling region, the expectation value of the horizon function is suggested to be zero or negative.
The first test of the Kugo-Ojima colour confinement criterion by the lattice Landau gauge QCD simulation is performed. The parameter u which is expected to be -1δ^a_b in the continuum theory was found to be -0.7δ^a_b in the strong coupling region. The data is analyzed in connection with the theory of Zwanziger. In the weak coupling region, the expectation value of the horizon function is negative or consistent to 0.
A class of algorithms for the Landau gauge fixing is proposed, which makes the steepest ascent (SA) method be more efficient by concepts of genetic algorithm. Main concern is how to incorporate random gauge transformation (RGT) %, mutation in genetic algorithm (GA) terminology, to gain higher achievement of the minimal Landau gauge fixing, and to keep lower time consumption. One of these algorithms uses the block RGT, and another uses RGT controlled by local fitness density, and the last uses RGT determined by Ising Monte Carlo process. We tested these algorithms on SU(2) lattice gauge theory in 4 dimension with small $β$s, 2.0, 1.75 and 1.5, and report improvements in hit rate and/or in time consumption, compared to other methods.
The gluon propagator in the Landau gauge lattice QCD simulation of quenched 8^3 x 16 lattice is measured. The data suggests the confinement mechanism of the Gribov-Zwanziger theory.
The Landau gauge fixing algorithm in the new definition of gauge fields is presented. In this algorithm a new solver of the Poisson equations based on the Green's function method is used. Its numerical performance of the gauge fixing algorithm is presented. Performance of the smeared gauge fixing in SU(3) is also investigated.
The 2nd order Runge-Kutta scheme Langevin simulation of unquenched QCD in pseudofermion method derived from our general theory shows a behaviour as a function of the Langevin step t better than the Fukugita,Oyanagi,Ukawa's scheme.
New partial differential equations for the Wiener-Hermite expansions of the Langevin (stochastic) transitions are formulated. They are solved recursively in full order series solutions with respect to $\sqrt{t}$. A sort of 'gauge' degrees of freedom (arbitrariness) involved in the solutions are analyzed and clarified. The Wiener-Hermite expansions play important roles as basic elements of numerical simulations of the Langevin equations. Specific solutions within some orders are presented as examples. These expansions giving integral representations of the Fokker-Planck evolution kernels, similar formulations are possible for the imaginary time Hamiltonian evolution kernels as well.
Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.
A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling parameters, which makes the present method especially suitable for parallel and pipeline vector processing machines. Results of computer runs are presented to illustrate the efficiency. An idea to find such algorithms is also presented, which may be applicable to other distributions of interest in Monte Carlo simulations.