2,461 research outputs found
The Maximal Invariance Group of Newtons's Equations for a Free Point Particle
The maximal invariance group of Newton's equations for a free nonrelativistic
point particle is shown to be larger than the Galilei group. It is a
semi-direct product of the static (nine-parameter) Galilei group and an
group containing time-translations, dilations and a one-parameter
group of time-dependent scalings called {\it expansions}. This group was first
discovered by Niederer in the context of the free Schr\"odinger equation. We
also provide a road map from the free nonrelativistic point particle to the
equations of fluid mechanics to which the symmetry carries over. The hitherto
unnoticed part of the symmetry group for fluid mechanics gives a
theoretical explanation for an observed similarity between numerical
simulations of supernova explosions and numerical simulations of experiments
involving laser-induced implosions in inertial confinement plasmas. We also
give examples of interacting many body systems of point particles which have
this symmetry group.Comment: Plain TeX File: 15 Page
Pentaquark state in pole-dominated QCD sum rules
We propose a new approach in QCD sum rules applied for exotic hadrons with a
number of quarks, exemplifying the pentaquark Theta^{+} (I=0,J=1/2) in the
Borel sum rule. Our approach enables reliable extraction of the pentaquark
properties from the sum rule with good stability in a remarkably wide Borel
window. The appearance of its valid window originates from a favorable setup of
the correlation functions with the aid of it chirality of the interpolating
fields on the analogy of the Weinberg sum rule for the vector currents. Our
setup leads to large suppression of the continuum contributions which have
spoiled the Borel stability in the previous analyses, and consequently enhances
importance of the higher-dimensional contributions of the OPE, which are
indispensable for investigating the pentaquark properties. Implementing the OPE
analysis up to dimension 15, we find that the sum rules for the chiral-even and
odd parts independently give the Theta^{+} mass of 1.68 pm 0.22 GeV with
uncertainties of the condensate values. Our sum rule indeed gives rather flat
Borel curves almost independent of the continuum thresholds both for the mass
and pole residue. Finally, we also discuss possible isolation of the observed
states from the KN scattering state on view of chiral symmetry.Comment: 8 pages, 7 figure
Center Vortices, Instantons, and Confinement
We study the relation between center vortices and instantons in lattice QCD.Comment: 3 pages, 1 color figure, LaTeX209 using BoxedEPS and esprc2.sty
(provided); talk presented by J.W. Negele to be published in Lattice99
(Topology); email to [email protected]
Comparison of SO(3) and SU(2) lattice gauge theory
The Villain form of SO(3) lattice gauge theory is studied and compared to Wilson's SU(2) theory. The topological invariants in SO(3) which correspond to twisted boundary conditions in SU(2) are discussed and lattice observables are introduced for them. An apparent SO(3) phase with negative adjoint Polyakov loop is explained in terms of these observables. The electric twist free energy, an order parameter for the confinement-deconfinement transition, is measured in both theories to calibrate the temperature. The results indicate that lattices with about 700^4 sites or larger will be needed to study the SO(3) confined phase. Alternative actions are discussed and an analytic path connecting SO(3) and SU(2) lattice gauge theory at weak coupling is exhibited. The relevance for confinement of the centre of the gauge group is discussed
The Path Integral for 1+1-dimensional QCD
We derive a path integral expression for the transition amplitude in
1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after
quantization leads to a formulation in terms of gauge invariant but curvilinear
variables. Remainders of the curved space are Jacobians, an effective
potential, and sign factors just as for the problem of a particle in a box.
Based on this result we derive a Faddeev-Popov like expression for the
transition amplitude avoiding standard infinities that are caused by
integrations over gauge equivalent configurations.Comment: 16 pages, LaTeX, 3 PostScript figures, uses epsf.st
The ground state of three quarks
We measure the static three-quark potential in SU(3) lattice gauge theory
with improved accuracy, by using all available technical refinements, including
Luscher-Weisz exponential variance reduction. Together with insight gained from
3-state Potts model simulations, our results allow us to sort out the merits of
the Delta- and Y-ansaetze.Comment: 3 pages, 4 figures, talk presented at Lattice2002(topology
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