6,418 research outputs found
The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
We complete our study of non-Abelian gauge theories in the framework of
Epstein-Glaser approach to renormalization theory including in the model an
arbitrary number of Dirac Fermions. We consider the consistency of the model up
to the third order of the perturbation theory. In the second order we obtain
pure group theoretical relations expressing a representation property of the
numerical coefficients appearing in the left and right handed components of the
interaction Lagrangian. In the third order of the perturbation theory we obtain
the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate
The Interaction of Quantum Gravity with Matter
The interaction of (linearized) gravitation with matter is studied in the
causal approach up to the second order of perturbation theory. We consider the
generic case and prove that gravitation is universal in the sense that the
existence of the interaction with gravitation does not put new constraints on
the Lagrangian for lower spin fields. We use the formalism of quantum off-shell
fields which makes our computation more straightforward and simpler.Comment: 25 page
Kink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation
We have examined the dynamical behavior of the kink solutions of the
one-dimensional sine-Gordon equation in the presence of a spatially periodic
parametric perturbation. Our study clarifies and extends the currently
available knowledge on this and related nonlinear problems in four directions.
First, we present the results of a numerical simulation program which are not
compatible with the existence of a radiative threshold, predicted by earlier
calculations. Second, we carry out a perturbative calculation which helps
interpret those previous predictions, enabling us to understand in depth our
numerical results. Third, we apply the collective coordinate formalism to this
system and demonstrate numerically that it accurately reproduces the observed
kink dynamics. Fourth, we report on a novel occurrence of length scale
competition in this system and show how it can be understood by means of linear
stability analysis. Finally, we conclude by summarizing the general physical
framework that arises from our study.Comment: 19 pages, REVTeX 3.0, 24 figures available from A S o
Does the Chapman--Enskog expansion for sheared granular gases converge?
The fundamental question addressed in this paper is whether the partial
Chapman--Enskog expansion of the shear stress converges or not for a gas of
inelastic hard spheres. By using a simple kinetic model it is shown that, in
contrast to the elastic case, the above series does converge, the radius of
convergence increasing with inelasticity. It is argued that this paradoxical
conclusion is not an artifact of the kinetic model and can be understood in
terms of the time evolution of the scaled shear rate in the uniform shear flow.Comment: 4 pages, 1 table, 2 figures; v2: minor changes,Fig. 2 redon
Empty pentagons in point sets with collinearities
An empty pentagon in a point set P in the plane is a set of five points in P
in strictly convex position with no other point of P in their convex hull. We
prove that every finite set of at least 328k^2 points in the plane contains an
empty pentagon or k collinear points. This is optimal up to a constant factor
since the (k-1)x(k-1) grid contains no empty pentagon and no k collinear
points. The previous best known bound was doubly exponential.Comment: 15 pages, 11 figure
Spectral Statistics for the Dirac Operator on Graphs
We determine conditions for the quantisation of graphs using the Dirac
operator for both two and four component spinors. According to the
Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry
the energy level statistics are expected, in the semiclassical limit, to
correspond to those of random matrices from the Gaussian symplectic ensemble.
This is confirmed by numerical investigation. The scattering matrix used to
formulate the quantisation condition is found to be independent of the type of
spinor. We derive an exact trace formula for the spectrum and use this to
investigate the form factor in the diagonal approximation
The WARPS Survey. VIII. Evolution of the Galaxy Cluster X-ray Luminosity Function
We present measurements of the galaxy cluster X-ray Luminosity Function (XLF)
from the Wide Angle ROSAT Pointed Survey (WARPS) and quantify its evolution.
WARPS is a serendipitous survey of the central region of ROSAT pointed
observations and was carried out in two phases (WARPS-I and WARPS-II). The
results here are based on a final sample of 124 clusters, complete above a flux
limit of 6.5 10E-15 erg/s/cm2, with members out to redshift z ~ 1.05, and a sky
coverage of 70.9 deg2. We find significant evidence for negative evolution of
the XLF, which complements the majority of X-ray cluster surveys. To quantify
the suggested evolution, we perform a maximum likelihood analysis and conclude
that the evolution is driven by a decreasing number density of high luminosity
clusters with redshift, while the bulk of the cluster population remains nearly
unchanged out to redshift z ~ 1.1, as expected in a low density Universe. The
results are found to be insensitive to a variety of sources of systematic
uncertainty that affect the measurement of the XLF and determination of the
survey selection function. We perform a Bayesian analysis of the XLF to fully
account for uncertainties in the local XLF on the measured evolution, and find
that the detected evolution remains significant at the 95% level. We observe a
significant excess of clusters in the WARPS at 0.1 < z < 0.3 and LX ~ 2 10E42
erg/s compared with the reference low-redshift XLF, or our Bayesian fit to the
WARPS data. We find that the excess cannot be explained by sample variance, or
Eddington bias, and is unlikely to be due to problems with the survey selection
function.Comment: 13 pages, 12 figures, accepted for publication in MNRA
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