7,286 research outputs found
On the singular homology of one class of simply-connected cell-like spaces
In our earlier papers we constructed examples of 2-dimensional nonaspherical
simply-connected cell-like Peano continua, called {\sl Snake space}. In the
sequel we introduced the functor defined on the category of all
spaces with base points and continuous mappings. For the circle , the
space is a Snake space. In the present paper we study the
higher-dimensional homology and homotopy properties of the spaces
for any path-connected compact spaces
Gauge Group and Topology Change
The purpose of this study is to examine the effect of topology change in the
initial universe. In this study, the concept of -cobordism is introduced to
argue about the topology change of the manifold on which a transformation group
acts. This -manifold has a fiber bundle structure if the group action is
free and is related to the spacetime in Kaluza-Klein theory or
Einstein-Yang-Mills system. Our results revealed that fundamental processes of
compactification in -manifolds. In these processes, the initial high
symmetry and multidimensional universe changes to present universe by the
mechanism which lowers the dimensions and symmetries.Comment: 8 page
On the homology of the Harmonic Archipelago
We calculate the singular homology and \v{C}ech cohomology groups of the
Harmonic archipelago. As a corollary, we prove that this space is not homotopy
equivalent to the Griffiths space. This is interesting in view of Eda's proof
that the first singular homology groups of these spaces are isomorphic
Cauchy's formulas for random walks in bounded domains
Cauchy's formula was originally established for random straight paths
crossing a body and basically relates the average
chord length through to the ratio between the volume and the surface of the
body itself. The original statement was later extended in the context of
transport theory so as to cover the stochastic paths of Pearson random walks
with exponentially distributed flight lengths traversing a bounded domain. Some
heuristic arguments suggest that Cauchy's formula may also hold true for
Pearson random walks with arbitrarily distributed flight lengths. For such a
broad class of stochastic processes, we rigorously derive a generalized
Cauchy's formula for the average length travelled by the walkers in the body,
and show that this quantity depends indeed only on the ratio between the volume
and the surface, provided that some constraints are imposed on the entrance
step of the walker in . Similar results are obtained also for the average
number of collisions performed by the walker in , and an extension to
absorbing media is discussed.Comment: 12 pages, 6 figure
Schwinger Model Green functions with topological effects
The fermion propagator and the 4-fermion Green function in the massless QED2
are explicitly found with topological effects taken into account. The
corrections due to instanton sectors k=+1,-1, contributing to the propagator,
are shown to be just the homogenous terms admitted by the Dyson-Schwinger
equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are
included into consideration. The quark condensates are then calculated and are
shown to satisfy cluster property. The theta-dependence exhibited by the Green
functions corresponds to and may be removed by performing certain chiral gauge
transformation.Comment: 16 pages, in REVTE
Direct instantons, topological charge screening and QCD glueball sum rules
Nonperturbative Wilson coefficients of the operator product expansion (OPE)
for the spin-0 glueball correlators are derived and analyzed. A systematic
treatment of the direct instanton contributions is given, based on realistic
instanton size distributions and renormalization at the operator scale. In the
pseudoscalar channel, topological charge screening is identified as an
additional source of (semi-) hard nonperturbative physics. The screening
contributions are shown to be vital for consistency with the anomalous axial
Ward identity, and previously encountered pathologies (positivity violations
and the disappearance of the 0^{-+} glueball signal) are traced to their
neglect. On the basis of the extended OPE, a comprehensive quantitative
analysis of eight Borel-moment sum rules in both spin-0 glueball channels is
then performed. The nonperturbative OPE coefficients turn out to be
indispensable for consistent sum rules and for their reconciliation with the
underlying low-energy theorems. The topological short-distance physics strongly
affects the sum rule results and reveals a rather diverse pattern of glueball
properties. New predictions for the spin-0 glueball masses and decay constants
and an estimate of the scalar glueball width are given, and several
implications for glueball structure and experimental glueball searches are
discussed.Comment: 49 pages, 8 figure
INTEGRAL observations of the blazar Mrk 421 in outburst (Results of a multi-wavelength campaign)
We report the results of a multi-wavelength campaign on the blazar Mrk 421
during outburst. We observed four strong flares at X-ray energies that were not
seen at other wavelengths (partially because of missing data). From the fastest
rise in the X-rays, an upper limit could be derived on the extension of the
emission region. A time lag between high-energy and low-energy X-rays was
observed, which allowed an estimation of the magnetic-field strength. The
spectral analysis of the X-rays revealed a slight spectral hardening of the
low-energy (3 - 43 keV) spectral index. The hardness-ratio analysis of the
Swift-XRT (0.2 - 10 keV) data indicated a small correlation with the intensity;
i. e., a hard-to-soft evolution was observed. At the energies of IBIS/ISGRI (20
- 150 keV), such correlations are less obvious. A multiwavelength spectrum was
composed and the X-ray and bolometric luminosities are calculated.Comment: 15 pages, 18 figures; accepted by Astronomy & Astrophysic
-to-Glueball form factor and Glueball production in decays
We investigate transition form factors of meson decays into a scalar
glueball in the light-cone formalism. Compared with form factors of to
ordinary scalar mesons, the -to-glueball form factors have the same power in
the expansion of . Taking into account the leading twist light-cone
distribution amplitude, we find that they are numerically smaller than those
form factors of to ordinary scalar mesons. Semileptonic ,
and decays are subsequently investigated. We
also analyze the production rates of scalar mesons in semileptonic decays
in the presence of mixing between scalar and glueball states. The
glueball production in meson decays is also investigated and the LHCb
experiment may discover this channel. The sizable branching fraction in , or could be a clear signal for a scalar glueball
state.Comment: 17 pages, 3 figure, revtex
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