Quantum Fluctuations of Particles and Fields in Smooth Path Integrals

An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with exp(-S) by appropriate methods. The weighted smooth paths reproduce properties of the ground state of the harmonic oscillator in one dimension with high accuracy. Quantum fluctuations of U(1) and SU(2) gauge fields in four dimensions are also evaluated in our approach.Comment: 4 pages, 1 figure, talk given at the 12th Asia Pacific Physics Conference of AAPPS (APPC12), Makuhari, Japan, 14-19 July 201

Framework for non-perturbative analysis of a Z(3)-symmetric effective theory of finite temperature QCD

We study a three dimensional Z(3)-symmetric effective theory of high temperature QCD. The exact lattice-continuum relations, needed in order to perform lattice simulations with physical parameters, are computed to order O(a^0) in lattice perturbation theory. Lattice simulations are performed to determine the phase structure of a subset of the parameter space.Comment: 28 pages, 11 figures; v3: references rearranged, typos corrected, figs changed, published versio

Lattice analysis for the energy scale of QCD phenomena

We formulate a new framework in lattice QCD to study the relevant energy scale of QCD phenomena. By considering the Fourier transformation of link variable, we can investigate the intrinsic energy scale of a physical quantity nonperturbatively. This framework is broadly available for all lattice QCD calculations. We apply this framework for the quark-antiquark potential and meson masses in quenched lattice QCD. The gluonic energy scale relevant for the confinement is found to be less than 1 GeV in the Landau or Coulomb gauge.Comment: 4 pages, 4 figure

Classes of confining gauge field configurations

We present a numerical method to compute path integrals in effective SU(2) Yang-Mills theories. The basic idea is to approximate the Yang-Mills path integral by summing over all gauge field configurations, which can be represented as a linear superposition of a small number of localized building blocks. With a suitable choice of building blocks many essential features of SU(2) Yang-Mills theory can be reproduced, particularly confinement. The analysis of our results leads to the conclusion that topological charge as well as extended structures are essential elements of confining gauge field configurations.Comment: 18 pages, 16 figures, several sections adde

Lattice energy sum rule and the trace anomaly

We show that the additional contribution to the Michael lattice energy sum rule pointed out recently, can be identified with the contribution to the field energy of a quark-antiquark pair arising from the trace anomaly of the energy momentum tensor

Stability of the pentaquark in a naive string model

The pentaquark is studied in a simple model of confinement where the quarks and the antiquark are linked by flux tubes of minimal cumulated length, and the Coulomb-like interaction, the spin-dependent terms and the antisymmetrization constraints are neglected.. The ground-state is found to be stable against spontaneous dissociation into a meson and a baryon, both in the case of five equal-mass constituents and for a static quark or antiquark surrounded by four equal masses.Comment: 8 pages, 2 figures, minor corrections, references added, to appear in Phys. Rev.

Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.Comment: 3 Figures. Version accepted in J. Phys.