1,832 research outputs found
Random matrix model at nonzero chemical potentials with anomaly effects
Phase diagram of the chiral random matrix model with U(1)A breaking term is
studied with the quark chemical potentials varied independently at zero
temperature, by taking the chiral and meson condensates as the order
parameters. Although, without the U(1)A breaking term, chiral transition of
each flavor can happen separately responding to its chemical potential, the
U(1)A breaking terms mix the chiral condensates and correlate the phase
transitions. In the three flavor case, we find that there are mixings between
the meson and chiral condensates due to the U(1)A anomaly, which makes the
meson condensed phase more stable. Increasing the hypercharge chemical
potential () with the isospin and quark chemical potentials (,
) kept small, we observe that the kaon condensed phase becomes the
ground state and at the larger the pion condense phase appears
unexpectedly, which is caused by the competition between the chiral restoration
and the meson condensation. The similar happens when and are
exchanged, and the kaon condensed phase becomes the ground state at larger
below the full chiral restoration.Comment: 12 pages, 8 figure
The back reaction and the effective Einstein's equation for the Universe with ideal fluid cosmological perturbations
We investigate the back reaction of cosmological perturbations on the
evolution of the Universe using the renormalization group method. Starting from
the second order perturbed Einstein's equation, we renormalize a scale factor
of the Universe and derive the evolution equation for the effective scale
factor which includes back reaction due to inhomogeneities of the Universe. The
resulting equation has the same form as the standard Friedman-Robertson-Walker
equation with the effective energy density and pressure which represent the
back reaction effect.Comment: 16 pages, to appear in Phys. Rev.
Back Reaction Problem in the Inflationary Universe
We investigate the back reaction of cosmological perturbations on an
inflationary universe using the renormalization-group method. The second-order
zero mode solution which appears by the nonlinearity of the Einstein equation
is regarded as a secular term of a perturbative expansion, we renormalized a
constant of integration contained in the background solution and absorbed the
secular term to this constant in a gauge-invariant manner. The resultant
renormalization-group equation describes the back reaction effect of
inhomogeneity on the background universe. For scalar type classical
perturbation, by solving the renormalization-group equation, we find that the
back reaction of the long wavelength fluctuation works as a positive spatial
curvature, and the short wavelength fluctuation works as a radiation fluid. For
the long wavelength quantum fluctuation, the effect of back reaction is
equivalent to a negative spatial curvature.Comment: 17 page
Asymptotic Freedom: From Paradox to Paradigm
Asymptotic freedom was developed as a response to two paradoxes: the
weirdness of quarks, and in particular their failure to radiate copiously when
struck; and the coexistence of special relativity and quantum theory, despite
the apparent singularity of quantum field theory. It resolved these paradoxes,
and catalyzed the development of several modern paradigms: the hard reality of
quarks and gluons, the origin of mass from energy, the simplicity of the early
universe, and the power of symmetry as a guide to physical law.Comment: 26 pages, 10 figures. Lecture on receipt of the 2004 Nobel Prize. v2:
typo (in Ohm's law) correcte
Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t Hooft Picture for Color Confinement
We study the Nambu-'t Hooft picture for color confinement in terms of the
abelianization of QCD and monopole condensation in the maximally abelian (MA)
gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon
amplitude is strongly suppressed, and then the off-diagonal gluon phase shows
strong randomness, which leads to rapid reduction of the off-diagonal gluon
correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian
Landau gauge, the Euclidean gluon propagator indicates a large effective mass
of the off-diagonal gluon as in the
intermediate distance as . Due to the
infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized
like nonabelian Higgs theories in the MA gauge. We investigate the
inter-monopole potential and the dual gluon field in the MA gauge, and
find longitudinal magnetic screening with 0.5 GeV in the infrared
region, which indicates the dual Higgs mechanism by monopole condensation. We
define the ``gluonic Higgs scalar field'' providing the MA projection, and find
the correspondence between its hedgehog singularity and the monopole location
in lattice QCD.Comment: Invited talk given at QCD02: High-Energy Physics International
Conference in Quantum Chromodynamics, Montpellier, France, 2-9 Jul 200
The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number
A regularization for the baryon number consistent with the energy in the
Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed
with the regularized baryon number constrained to unity. It is furthermore
demonstrated that this constraint prevents the soliton from collapsing when
scalar fields are allowed to be space dependent. In this scheme the scalar
fields actually vanish at the origin reflecting a partial restoration of chiral
symmetry. Also the influence of this constraint on some static properties of
baryons is discussed.Comment: 10 LaTeX pages 4 figures, report no UNITU-THEP-7/199
Volume Expansion of Swiss-Cheese Universe
In order to investigate the effect of inhomogeneities on the volume expansion
of the universe, we study modified Swiss-Cheese universe model. Since this
model is an exact solution of Einstein equations, we can get an insight into
non-linear dynamics of inhomogeneous universe from it. We find that
inhomogeneities make the volume expansion slower than that of the background
Einstein-de Sitter universe when those can be regarded as small fluctuations in
the background universe. This result is consistent with the previous studies
based on the second order perturbation analysis. On the other hand, if the
inhomogeneities can not be treated as small perturbations, the volume expansion
of the universe depends on the type of fluctuations. Although the volume
expansion rate approaches to the background value asymptotically, the volume
itself can be finally arbitrarily smaller than the background one and can be
larger than that of the background but there is an upper bound on it.Comment: 22 pages, 7 figures, to be submitted to Phys. Rev.
The Role of Monopoles for Color Confinement
We study the role of the monopole for color confinement by using the monopole
current system. For the self-energy of the monopole current less than
ln, long and complicated monopole world-lines appear and the Wilson
loop obeys the area law, and therefore the monopole current system almost
reproduces essential features of confinement properties in the long-distance
physics. In the short-distance physics, however, the monopole-current theory
would become nonlocal due to the monopole size effect. This monopole size would
provide a critical scale of QCD in terms of the dual Higgs mechanism.Comment: 3 pages LaTeX, 3 figures, uses espcrc2.sty, Talk presented at
lattice97, Edinburgh, Scotland, July. 199
Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges
We investigate in detail "instantaneous interquark potentials", interesting
gauge-dependent quantities defined from the spatial correlators of the temporal
link-variable , in generalized Landau gauge using SU(3) quenched lattice
QCD. The instantaneous Q potential has no linear part in the
Landau gauge, and it is expressed by the Coulomb plus linear potential in the
Coulomb gauge, where the slope is 2-3 times larger than the physical string
tension. Using the generalized Landau gauge, we find that the instantaneous
potential can be continuously described between the Landau and the Coulomb
gauges, and its linear part rapidly grows in the neighborhood of the Coulomb
gauge. We also investigate the instantaneous 3Q potential in the generalized
Landau gauge, and obtain similar results to the Q case. -length
terminated Polyakov-line correlators and their corresponding "finite-time
potentials" are also investigated in generalized Landau gauge
- …