971 research outputs found
Discreteness of the volume of space from Bohr-Sommerfeld quantization
A major challenge for any theory of quantum gravity is to quantize general
relativity while retaining some part of its geometrical character. We present
new evidence for the idea that this can be achieved by directly quantizing
space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron
and show that it reproduces the quantization of a grain of space found in loop
gravity.Comment: 4 pages, 4 figures; v2, to appear in PR
The U(1)A anomaly in noncommutative SU(N) theories
We work out the one-loop anomaly for noncommutative SU(N) gauge
theories up to second order in the noncommutative parameter .
We set and conclude that there is no breaking of the classical
symmetry of the theory coming from the contributions that are either
linear or quadratic in . Of course, the ordinary anomalous
contributions will be still with us. We also show that the one-loop
conservation of the nonsinglet currents holds at least up to second order in
. We adapt our results to noncommutative gauge theories with
SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde
Effects of Noise on Galaxy Isophotes
The study of shapes of the images of objects is an important issue not only
because it reveals its dynamical state but also it helps to understand the
object's evolutionary history. We discuss a new technique in cosmological image
analysis which is based on a set of non-parametric shape descriptors known as
the Minkowski Functionals (MFs). These functionals are extremely versatile and
under some conditions give a complete description of the geometrical properties
of objects. We believe that MFs could be a useful tool to extract information
about the shapes of galaxies, clusters of galaxies and superclusters. The
information revealed by MFs can be utilized along with the knowledge obtained
from currently popular methods and thus could improve our understanding of the
true shapes of cosmological objects.Comment: 3 pages, 1 figure, to appear in "The IGM/Galaxy Connection - The
Distribution of Baryons at z=0" Conference Proceeding
QCD Tests of the Puzzling Scalar Mesons
Motivated by several recent data, we test the QCD spectral sum rules (QSSR)
predictions based on different proposals (\bar qq, \bar q\bar q qq, and
gluonium) for the nature of scalar mesons. In the I=1 and 1/2 channels, the
unusual (wrong) splitting between the a_0(980) and \kappa(900) and the a_0(980)
width can be understood from QSSR within a \bar qq assignement. However, none
of the \bar qq and \bar q\bar q qq results can explain the large \kappa width,
which may suggest that it can result from a strong interference with
non-resonant backgrounds. In the I=0 channel, QSSR and some low-energy theorems
(LET) require the existence of a low mass gluonium \sigma_B(1 GeV) coupled
strongly to Goldstone boson pairs which plays in the U(1)_V channel, a similar
role than the \eta' for the value of the U(1)_A topological charge. The
observed \sigma(600) and f_0(980) mesons result from a maximal mixing between
the gluonium \sigma_B and \bar qq(1 GeV) mesons, a mixing scheme which passes
several experimental tests. OZI violating J/\psi--> \phi\pi^+\pi^-, D_s--> 3\pi
decays and J/\psi--> \gamma S glueball filter processes may indicate that most
of the I=0 mesons above 1 GeV have important gluonium in their wave functions.
We expect that the f_0(1500), f_0(1710) and f_0(1790) have significant gluonium
component in their wave functions, while the f_0(1370) is mostly \bar qq. Tests
of these results can be provided by the measurements of the pure gluonium
\eta'\eta and 4\pi specific U(1)_A decay channels.Comment: Version to appear in Phys. Rev. D (one previous figure corrupted
Hadronic structure aspects of decays
As is known from previous studies the lepton number violating decays have good prospects to probe new physics beyond the
Standard Model and provide valuable information on neutrino masses and mixing.
We analyze these processes with an emphasis on their hadronic structure
aspects applying relativistic constituent quark model. We conclude that the
previously ignored contribution associated with the t-channel Majorana neutrino
exchange is comparable with the s-channel one in a wide range of neutrino
masses. We also estimated model independent absolute upper bounds on neutrino
contribution to these decays.Comment: 15 pages, 1 figure. Version to appear in PRD, normalization factor in
Eq. (25) is correcte
An X-ray absorption analysis of the high-velocity system in NGC 1275
We present an X-ray absorption analysis of the high-velocity system (HVS) in
NGC 1275 using results from a deep 200 ks Chandra observation. We are able to
describe the morphology of the HVS in more detail than ever before. We present
an HST image for comparison, and note close correspondence between the deepest
X-ray absorption and the optical absorption. A column density map of the HVS
shows an average column density NH of 1x10^21 cm^-2 with a range from ~5x10^20
to 5x10^21 cm^-2. From the NH map we calculate a total mass for the absorbing
gas in the HVS of (1.32+-0.05)x10^9 solar masses at solar abundance. 75 per
cent of the absorbing mass is contained in the four regions of deepest
absorption. We examine temperature maps produced by spectral fitting and find
no direct evidence for shocked gas in the HVS. Using deprojection methods and
the depth of the observed absorption, we are able to put a lower limit on the
distance of the HVS from the nucleus of 57 kpc, showing that the HVS is quite
separate from the body of NGC 1275.Comment: 6 pages, 5 colour figures, accepted by MNRA
Estimates of the optimal density and kissing number of sphere packings in high dimensions
The problem of finding the asymptotic behavior of the maximal density of
sphere packings in high Euclidean dimensions is one of the most fascinating and
challenging problems in discrete geometry. One century ago, Minkowski obtained
a rigorous lower bound that is controlled asymptotically by , where
is the Euclidean space dimension. An indication of the difficulty of the
problem can be garnered from the fact that exponential improvement of
Minkowski's bound has proved to be elusive, even though existing upper bounds
suggest that such improvement should be possible. Using a
statistical-mechanical procedure to optimize the density associated with a
"test" pair correlation function and a conjecture concerning the existence of
disordered sphere packings [S. Torquato and F. H. Stillinger, Experimental
Math. {\bf 15}, 307 (2006)], the putative exponential improvement was found
with an asymptotic behavior controlled by . Using the same
methods, we investigate whether this exponential improvement can be further
improved by exploring other test pair correlation functions correponding to
disordered packings. We demonstrate that there are simpler test functions that
lead to the same asymptotic result. More importantly, we show that there is a
wide class of test functions that lead to precisely the same exponential
improvement and therefore the asymptotic form is much
more general than previously surmised.Comment: 23 pages, 4 figures, submitted to Phys. Rev.
The evolution of pebble size and shape in space and time
We propose a mathematical model which suggests that the two main geological
observations about shingle beaches, i.e. the emergence of predominant pebble
size ratios and strong segregation by size are interrelated. Our model is a
based on a system of ODEs called the box equations, describing the evolution of
pebble ratios. We derive these ODEs as a heuristic approximation of Bloore's
PDE describing collisional abrasion. While representing a radical
simplification of the latter, our system admits the inclusion of additional
terms related to frictional abrasion. We show that nontrivial attractors
(corresponding to predominant pebble size ratios) only exist in the presence of
friction. By interpreting our equations as a Markov process, we illustrate by
direct simulation that these attractors may only stabilized by the ongoing
segregation process.Comment: 22 pages, 8 figure
Bohr-Sommerfeld Quantization of Space
We introduce semiclassical methods into the study of the volume spectrum in
loop gravity. The classical system behind a 4-valent spinnetwork node is a
Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase
space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The
analysis shows a remarkable quantitative agreement with the volume spectrum
computed in loop gravity. Moreover, it provides new geometrical insights into
the degeneracy of this spectrum and the maximum and minimum eigenvalues of the
volume on intertwiner space.Comment: 32 pages, 10 figure
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