637 research outputs found
Eliashberg's proof of Cerf's theorem
Following a line of reasoning suggested by Eliashberg, we prove Cerf's
theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To
this end we develop a moduli-theoretic version of Eliashberg's
filling-with-holomorphic-discs method.Comment: 32 page
Scalar field propagation in the phi^4 kappa-Minkowski model
In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model
based on the kappa-deformed star product, ({*}_h). The action is modified by
expanding up to linear order in the kappa-deformation parameter a, producing an
effective model on commutative spacetime. For the computation of the tadpole
diagram contributions to the scalar field propagation/self-energy, we
anticipate that statistics on the kappa-Minkowski is specifically
kappa-deformed. Thus our prescription in fact represents hybrid approach
between standard quantum field theory (QFT) and NCQFT on the kappa-deformed
Minkowski spacetime, resulting in a kappa-effective model. The propagation is
analyzed in the framework of the two-point Green's function for low,
intermediate, and for the Planckian propagation energies, respectively.
Semiclassical/hybrid behavior of the first order quantum correction do show up
due to the kappa-deformed momentum conservation law. For low energies, the
dependence of the tadpole contribution on the deformation parameter a drops out
completely, while for Planckian energies, it tends to a fixed finite value. The
mass term of the scalar field is shifted and these shifts are very different at
different propagation energies. At the Planckian energies we obtain the
direction dependent kappa-modified dispersion relations. Thus our
kappa-effective model for the massive scalar field shows a birefringence
effect.Comment: 23 pages, 2 figures; To be published in JHEP. Minor typos corrected.
Shorter version of the paper arXiv:1107.236
Scalar field theory on -Minkowski space-time and Doubly Special Relativity
In this paper we recall the construction of scalar field action on
-Minkowski space-time and investigate its properties. In particular we
show how the co-product of -Poincar\'e algebra of symmetries arises
from the analysis of the symmetries of the action, expressed in terms of
Fourier transformed fields. We also derive the action on commuting space-time,
equivalent to the original one. Adding the self-interaction term we
investigate the modified conservation laws. We show that the local interactions
on -Minkowski space-time give rise to 6 inequivalent ways in which
energy and momentum can be conserved at four-point vertex. We discuss the
relevance of these results for Doubly Special Relativity.Comment: 17 pages; some editing done, final version to be published in Int. J.
Mod. Phys.
-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
The -deformed Poincar{\'e} superalgebra written in Hopf
superalgebra form is transformed to the basis with classical Lorentz subalgebra
generators. We show that in such a basis the -deformed Poincare
superalgebra can be written as graded bicrossproduct. We show that the
-deformed superalgebra acts covariantly on -deformed
chiral superspace.Comment: 13 pages, late
Two Coupled Harmonic Oscillators on Non-commutative Plane
We investigate a system of two coupled harmonic oscillators on the
non-commutative plane \RR^2_{\theta} by requiring that the spatial coordinates
do not commute. We show that the system can be diagonalized by a suitable
transformation, i.e. a rotation with a mixing angle \alpha. The obtained
eigenstates as well as the eigenvalues depend on the non-commutativity
parameter \theta. Focusing on the ground state wave function before the
transformation, we calculate the density matrix \rho_0(\theta) and find that
its traces {\rm Tr}(\rho_{0}(\theta)) and {\rm Tr}(\rho_0^2(\theta)) are not
affected by the non-commutativity. Evaluating the Wigner function on
\RR^2_{\theta} confirms this. The uncertainty relation is explicitly determined
and found to depend on \theta. For small values of \theta, the relation is
shifted by a \theta^2 term, which can be interpreted as a quantum correction.
The calculated entropy does not change with respect to the normal case. We
consider the limits \alpha=1 and \alpha={\pi\over 2}. In first case, by
identifying \theta to the squared magnetic length, one can recover basic
features of the Hall system.Comment: 15 pages, 1 figur
Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
We study systematically, through two loops, the divergence structure of the
supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By
introducing a spurion field to represent the supersymmetry breaking term F^3 we
are able to perform our calculations using conventional supergraph techniques.
Divergent terms proportional to F, F^2 and F^3 are produced (the first two are
to be expected on general grounds) but no higher-point divergences are found.
By adding ab initio F and F^2 terms to the original lagrangian we render the
model renormalizable. We determine the renormalization constants and beta
functions through two loops, thus making it possible to study the
renormalization group flow of the nonanticommutation parameter.Comment: 36 pages, 25 figures, Latex fil
Doubly Special Relativity and de Sitter space
In this paper we recall the construction of Doubly Special Relativity (DSR)
as a theory with energy-momentum space being the four dimensional de Sitter
space. Then the bases of the DSR theory can be understood as different
coordinate systems on this space. We investigate the emerging geometrical
picture of Doubly Special Relativity by presenting the basis independent
features of DSR that include the non-commutative structure of space-time and
the phase space algebra. Next we investigate the relation between our geometric
formulation and the one based on quantum -deformations of the
Poincar\'e algebra. Finally we re-derive the five-dimensional differential
calculus using the geometric method, and use it to write down the deformed
Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde
Poincare covariant mechanics on noncommutative space
The Dirac approach to constrained systems can be adapted to construct
relativistic invariant theories on a noncommutative (NC) space. As an example,
we propose and discuss relativistic invariant NC particle coupled to
electromagnetic field by means of the standard term . Poincare
invariance implies deformation of the free particle NC algebra in the
interaction theory. The corresponding corrections survive in the
nonrelativistic limit.Comment: 7 pages, JHEP style, final versio
A human colonic crypt culture system to study regulation of stem cell-driven tissue renewal and physiological function
The intestinal epithelium is one of the most rapidly renewing tissues in the human body and fulfils vital physiological roles such as barrier function and transport of nutrients and fluid. Investigation of gut epithelial physiology in health and disease has been hampered by the lack of ex vivo models of the native human intestinal epithelium. Recently, remarkable progress has been made in defining intestinal stem cells and in generating intestinal organoid cultures. In parallel, we have developed a 3D culture system of the native human colonic epithelium that recapitulates the topological hierarchy of stem cell-driven tissue renewal and permits the physiological study of native polarized epithelial cells. Here we describe methods to establish 3D cultures of intact human colonic crypts and conduct real-time imaging of intestinal tissue renewal, cellular signalling, and physiological function, in conjunction with manipulation of gene expression by lentiviral or adenoviral transduction. Visualization of mRNA- and protein-expression patterns in cultured human colonic crypts, and cross-validation with crypts derived from fixed mucosal biopsies, is also described. Alongside studies using intestinal organoids, the near-native human colonic crypt culture model will help to bridge the gap that exists between investigation of colon cancer cell lines and/or animal (tissue) studies, and progression to clinical trials. To this end, the near native human colonic crypt model provides a platform to aid the development of novel strategies for the prevention of inflammatory bowel disease and cancer
Longitudinal borehole functionality in 15 rural Ghanaian towns from three groundwater quality clusters
OBJECTIVE: In sub-Saharan Africa, 45% of the rural population uses boreholes (BHs). Despite recent gains in improved water access and coverage, parallel use of unimproved sources persists. Periodic infrastructure disrepair contributes to non-exclusive use of BHs. Our study describes functionality of BHs in 2014, 2015, and 2016 in 15 rural towns in the Eastern Region of Ghana sourced from three groundwater quality clusters (high iron, high salinity, and control). We also assess factors affecting cross-sectional and longitudinal functionality using logistic regression. RESULTS: BH functionality rates ranged between 81 and 87% and were similar across groundwater quality clusters. Of 51 BHs assessed in all three years, 34 (67%) were consistently functional and only 3 (6%) were consistently broken. There was a shift toward proactive payment for water over the course of the study in the control and high-salinity clusters. Payment mechanism, population served, presence of nearby alternative water sources, and groundwater quality cluster were not significant predictors of cross-sectional or longitudinal BH functionality. However, even in the high iron cluster, where water quality is poor and no structured payment mechanism for water exists, BHs are maintained, showing that they are important community resources
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