9,642 research outputs found
A note on the convexity number for complementary prisms
In the geodetic convexity, a set of vertices of a graph is
if all vertices belonging to any shortest path between two
vertices of lie in . The cardinality of a maximum proper convex
set of is the of . The
of a graph arises from the
disjoint union of the graph and by adding the edges of a
perfect matching between the corresponding vertices of and .
In this work, we we prove that the decision problem related to the convexity
number is NP-complete even restricted to complementary prisms, we determine
when is disconnected or is a cograph, and we
present a lower bound when .Comment: 10 pages, 2 figure
Renormalization in a Lorentz-violating model and higher-order operators
The renormalization in a Lorentz-breaking scalar-spinor higher-derivative
model involving self-interaction and the Yukawa-like coupling is
studied. We explicitly de- monstrate that the convergence is improved in
comparison with the usual scalar-spinor model, so, the theory is
super-renormalizable, with no divergences beyond four loops. We compute the
one-loop corrections to the propagators for the scalar and fermionic fields and
show that in the presence of higher-order Lorentz invariance violation, the
poles that dominate the physical theory, are driven away from the standard
on-shell pole mass due to radiatively induced lower dimensional operators. The
new operators change the standard gamma-matrix structure of the two-point
functions, introduce large Lorentz-breaking corrections and lead to
modifications in the renormalization conditions of the theory. We found the
physical pole mass in each sector of our model.Comment: 20 pages, 5 figures. New version with modifications in the
renormalized Lagrangian. To be published in EPJ
On the duality in four-dimensional Lorentz-breaking field theories
We consider new issues of duality in four-dimensional Lorentz-breaking field
theories. In particular, we demonstrate that the arising of the aether-like
Lorentz-breaking term is necessary in order for the 4D models to display the
duality analog between the MCS and self-dual models in 3D. We further study the
dispersion relations in both theories and discuss the physical contents of the
models involved in this new dualilty.Comment: 16 page
Dynamical Lorentz and CPT symmetry breaking in a 4D four-fermion model
In a 4D chiral Thirring model we analyse the possibility that radiative
corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By
studying the effective potential, we verified that the chiral current
may assume a nonzero vacuum expectation
value which triggers the Lorentz and CPT violations. Furthermore, by making
fluctuations on the minimum of the potential we dynamically induce a bumblebee
like model containing a Chern-Simons term.Comment: Small modifications in the text and new references added, 12 pages, 4
figures, revtex4. To appear in Phys. Rev.
The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions
We study the nonrelativistic limit of the theory of a quantum Chern--Simons
field minimally coupled to Dirac fermions. To get the nonrelativistic effective
Lagrangian one has to incorporate vacuum polarization and anomalous magnetic
moment effects. Besides that, an unsuspected quartic fermionic interaction may
also be induced. As a by product, the method we use to calculate loop diagrams,
separating low and high loop momenta contributions, allows to identify how a
quantum nonrelativistic theory nests in a relativistic one.Comment: 18 pages, 8 figures, Late
Dynamical analysis of the cluster pair: A3407 + A3408
We carried out a dynamical study of the galaxy cluster pair A3407 \& A3408
based on a spectroscopic survey obtained with the 4 meter Blanco telescope at
the CTIO, plus 6dF data, and ROSAT All-Sky-Survey. The sample consists of 122
member galaxies brighter than . Our main goal is to probe the galaxy
dynamics in this field and verify if the sample constitutes a single galaxy
system or corresponds to an ongoing merging process. Statistical tests were
applied to clusters members showing that both the composite system A3407 +
A3408 as well as each individual cluster have Gaussian velocity distribution. A
velocity gradient of was identified around
the principal axis of the projected distribution of galaxies, indicating that
the global field may be rotating. Applying the KMM algorithm to the
distribution of galaxies we found that the solution with two clusters is better
than the single unit solution at the 99\% c.l. This is consistent with the
X-ray distribution around this field, which shows no common X-ray halo
involving A3407 and A3408. We also estimated virial masses and applied a
two-body model to probe the dynamics of the pair. The more likely scenario is
that in which the pair is gravitationally bound and probably experiences a
collapse phase, with the cluster cores crossing in less than 1
Gyr, a pre-merger scenario. The complex X-ray morphology, the gas temperature,
and some signs of galaxy evolution in A3408 suggests a post-merger scenario,
with cores having crossed each other Gyr ago, as an
alternative solution.Comment: 17 pages, 12 figures, submitted to MNRAS, accepted 2016 May 9.
Received 2016 May 9; in original form 2016 April 1
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