45 research outputs found
Stability of the Magnetic Monopole Condensate in three- and four-colour QCD
It is argued that the ground state of three- and four-colour QCD contains a
monopole condensate, necessary for the dual Meissner effect to be the mechanism
of confinement, and support its stability on the grounds that it gives the
off-diagonal gluons an effective mass sufficient to remove the unstable ground
state mode.Comment: jhep.cls, typos corrected, references added, some content delete
Entropy Crisis, Ideal Glass Transition and Polymer Melting: Exact Solution on a Husimi Cactus
We introduce an extension of the lattice model of melting of semiflexible
polymers originally proposed by Flory. Along with a bending penalty, present in
the original model and involving three sites of the lattice, we introduce an
interaction energy that corresponds to the presence of a pair of parallel bonds
and a second interaction energy associated with the presence of a hairpin turn.
Both these new terms represent four-site interactions. The model is solved
exactly on a Husimi cactus, which approximates a square lattice. We study the
phase diagram of the system as a function of the energies. For a proper choice
of the interaction energies, the model exhibits a first-order melting
transition between a liquid and a crystalline phase. The continuation of the
liquid phase below this temperature gives rise to a supercooled liquid, which
turns continuously into a new low-temperature phase, called metastable liquid.
This liquid-liquid transition seems to have some features that are
characteristic of the critical transition predicted by the mode-coupling
theory.Comment: To be published in Physical Review E, 68 (2) (2003
(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and symmetry breaking in QCD
It is shown that an (anti-)self-dual homogeneous vacuum gluon field appears
in a natural way within the problem of calculation of the QCD partition
function in the form of Euclidean functional integral with periodic boundary
conditions. There is no violation of cluster property within this formulation,
nor are parity, color and rotational symmetries broken explicitly. The massless
limit of the product of the quark masses and condensates, , is calculated to all loop orders. This quantity
does not vanish and is proportional to the gluon condensate appearing due to
the nonzero strength of the vacuum gluon field. We conclude that the gluon
condensate can be considered as an order parameter both for confinement and
chiral symmetry breaking.Comment: 16 pages, LaTe
Monopole Condensation and Dimensional Transmutation in SU(2) QCD
We resolve the controversy on the stability of the monopole condensation in
the one-loop effective action of SU(2) QCD by calculating the imaginary part of
the effective action with two different methods at one-loop order. Our result
confirms that the effective action for the magnetic background has no imaginary
part but the one for the electric background has a negative imaginary part.
This assures that the monopole condensation is indeed stable, but the electric
background becomes unstable due to the pair-annihilation of gluons.Comment: 13 pages, 2 figure
On twisted Fourier analysis and convergence of Fourier series on discrete groups
We study norm convergence and summability of Fourier series in the setting of
reduced twisted group -algebras of discrete groups. For amenable groups,
F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson
summation holds for a large class of groups, including e.g. all Coxeter groups
and all Gromov hyperbolic groups. As a tool in our presentation, we introduce
notions of polynomial and subexponential H-growth for countable groups w.r.t.
proper scale functions, usually chosen as length functions. These coincide with
the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update
Meson masses within the model of induced nonlocal quark currents
The model of induced quark currents formulated in our recent paper (Phys.
Rev. D51, 176) is developed. The model being a kind of nonlocal extension of
the bosonization procedure is based on the hypothesis that the QCD vacuum is
realized by the (anti-)self-dual homogeneous gluon field. This vacuum field
provides the analytical quark confinement. It is shown that a particular form
of nonlocality of the quark and gluon propagators determined by the vacuum
field, an interaction of quark spin with the vacuum gluon field and a
localization of meson field at the center of masses of two quarks can explain
the distinctive features of meson spectrum: Regge trajectories of radial and
orbital excitations, mass splitting between pseudoscalar and vector mesons, the
asymptotic mass formulas in the heavy quark limit: for
quarkonia and for heavy-light mesons. With a minimal set
of parameters (quark masses, vacuum field strength and the quark-gluon coupling
constant) the model describes to within ten percent inaccuracy the masses and
weak decay constants of mesons from all qualitatively different regions of the
spectrum.Comment: 31 pages, LaTe
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TOPICS IN THE THEORY OF HEAVY QUARK SYSTEMS
Due to the kinematic and dynamic simplifications possible because of the large mass of heavy quark bound states, certain properties of these systems can be quantitatively analyzed within the framework of quantum chromodynamics. It is clear that dimensionally the size of the bound state is proportional to the inverse quark mass, and for very heavy quarkonia the radius of the system should become smaller than that of normal hadrons. When this small system interacts with external long wavelength field quanta, the natural expansion that results is of a multipole type, analogous to the familiar multipole expansion in electrodynamics. This multipole expansion has better convergence properties than the standard perturbative treatment in certain kinematic regimes, which opens up a new area for strong interaction physics calculations. More specifically, it is ideally suited to investigate soft non-perturbative effects in QCD which appear to be so crucial to present day phenomenology and the conjectured confinement mechanism