937 research outputs found
Approximate dual representation for Yang-Mills SU(2) gauge theory
An approximate dual representation for non-Abelian lattice gauge theories in
terms of a new set of dynamical variables, the plaquette occupation numbers
(PONs) that are natural numbers, is discussed. They are the expansion indices
of the local series of the expansion of the Boltzmann factors for every
plaquette of the Yang-Mills action. After studying the constraints due to gauge
symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a
PONs configuration the weight factor is given by Haar-measure integrals over
all links whose integrands are products of powers of plaquettes. Herein,
updates are limited to changes of the PON at a plaquette or all PONs on a
coordinate plane. The Markov chain transition probabilities are computed
employing truncated maximal trees and the Metropolis algorithm. The algorithm
performance is investigated with different types of updates for the plaquette
mean value over a large range of s. Using a lattice very good
agreement with a conventional heath bath algorithm is found for the strong and
weak coupling limits. Deviations from the latter being below 0.1% for . The mass of the lightest glueball is evaluated and
reproduces the results found in the literature
Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
A multiple scattering formulation is used to calculate the force, arising
from fluctuating scalar fields, between distinct bodies described by
-function potentials, so-called semitransparent bodies. (In the limit
of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We
obtain expressions for the Casimir energies between disjoint parallel
semitransparent cylinders and between disjoint semitransparent spheres. In the
limit of weak coupling, we derive power series expansions for the energy, which
can be exactly summed, so that explicit, very simple, closed-form expressions
are obtained in both cases. The proximity force theorem holds when the objects
are almost touching, but is subject to large corrections as the bodies are
moved further apart.Comment: 5 pages, 4 eps figures; expanded discussion of previous work and
additional references added, minor typos correcte
Hadronic current correlation functions at finite temperature in the NJL model
Recently there have been suggestions that for a proper description of
hadronic matter and hadronic correlation functions within the NJL model at
finite density/temperature the parameters of the model should be taken
density/temperature dependent. Here we show that qualitatively similar results
can be obtained using a cutoff-independent regularization of the NJL model. In
this regularization scheme one can express the divergent parts at finite
density/temperature of the amplitudes in terms of their counterparts in vacuum.Comment: Presented at 9th Hadron Physics and 8th Relativistic Aspects of
Nuclear Physics (HADRON-RANP 2004): A Joint Meeting on QCD and QGP, Angra dos
Reis, Rio de Janeiro, Brazil, 28 Mar - 3 Apr 200
Applications of M.G. Krein's Theory of Regular Symmetric Operators to Sampling Theory
The classical Kramer sampling theorem establishes general conditions that
allow the reconstruction of functions by mean of orthogonal sampling formulae.
One major task in sampling theory is to find concrete, non trivial realizations
of this theorem. In this paper we provide a new approach to this subject on the
basis of the M. G. Krein's theory of representation of simple regular symmetric
operators having deficiency indices (1,1). We show that the resulting sampling
formulae have the form of Lagrange interpolation series. We also characterize
the space of functions reconstructible by our sampling formulae. Our
construction allows a rigorous treatment of certain ideas proposed recently in
quantum gravity.Comment: 15 pages; v2: minor changes in abstract, addition of PACS numbers,
changes in some keywords, some few changes in the introduction, correction of
the proof of the last theorem, and addition of some comments at the end of
the fourth sectio
Influence of a Z+(1540) resonance on K+N scattering
The impact of a (I=0, J^P=1/2^+) Z^+(1540) resonance with a width of 5 MeV or
more on the K+N (I=0) elastic cross section and on the P01 phase shift is
examined within the KN meson-exchange model of the Juelich group. It is shown
that the rather strong enhancement of the cross section caused by the presence
of a Z^+ with the above properties is not compatible with the existing
empirical information on KN scattering. Only a much narrower Z^+ state could be
reconciled with the existing data -- or, alternatively, the Z^+ state must lie
at an energy much closer to the KN threshold.Comment: 9 pages, RevTeX, 3 eps figure
Cutoff-independent regularization of four-fermion interactions for color superconductivity
We implement a cutoff-independent regularization of four-fermion interactions
to calculate the color-superconducting gap parameter in quark matter. The
traditional cutoff regularization has difficulties for chemical potentials \mu
of the order of the cutoff \Lambda, predicting in particular a vanishing gap at
\mu \sim \Lambda. The proposed cutoff-independent regularization predicts a
finite gap at high densities and indicates a smooth matching with the weak
coupling QCD prediction for the gap at asymptotically high densities.Comment: 5 pages, 1 eps figure - Revised manuscript to match the published
pape
Multipeakons and a theorem of Stieltjes
A closed form of the multi-peakon solutions of the Camassa-Holm equation is
found using a theorem of Stieltjes on continued fractions. An explicit formula
is obtained for the scattering shifts.Comment: 6 page
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