14,189 research outputs found
Direct innervation of capillary endothelial cells in the lamina propria of the ferret stomach
Direct innervation of capillary endothelial cells in lamina propria of ferret stomac
A spin foam model for pure gauge theory coupled to quantum gravity
We propose a spin foam model for pure gauge fields coupled to Riemannian
quantum gravity in four dimensions. The model is formulated for the
triangulation of a four-manifold which is given merely combinatorially. The
Riemannian Barrett--Crane model provides the gravity sector of our model and
dynamically assigns geometric data to the given combinatorial triangulation.
The gauge theory sector is a lattice gauge theory living on the same
triangulation and obtains from the gravity sector the geometric information
which is required to calculate the Yang--Mills action. The model is designed so
that one obtains a continuum approximation of the gauge theory sector at an
effective level, similarly to the continuum limit of lattice gauge theory, when
the typical length scale of gravity is much smaller than the Yang--Mills scale.Comment: 18 pages, LaTeX, 1 figure, v2: details clarified, references adde
Uniqueness and Non-uniqueness in the Einstein Constraints
The conformal thin sandwich (CTS) equations are a set of four of the Einstein
equations, which generalize the Laplace-Poisson equation of Newton's theory. We
examine numerically solutions of the CTS equations describing perturbed
Minkowski space, and find only one solution. However, we find {\em two}
distinct solutions, one even containing a black hole, when the lapse is
determined by a fifth elliptic equation through specification of the mean
curvature. While the relationship of the two systems and their solutions is a
fundamental property of general relativity, this fairly simple example of an
elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte
Dual variables and a connection picture for the Euclidean Barrett-Crane model
The partition function of the SO(4)- or Spin(4)-symmetric Euclidean
Barrett-Crane model can be understood as a sum over all quantized geometries of
a given triangulation of a four-manifold. In the original formulation, the
variables of the model are balanced representations of SO(4) which describe the
quantized areas of the triangles. We present an exact duality transformation
for the full quantum theory and reformulate the model in terms of new variables
which can be understood as variables conjugate to the quantized areas. The new
variables are pairs of S^3-values associated to the tetrahedra. These
S^3-variables parameterize the hyperplanes spanned by the tetrahedra (locally
embedded in R^4), and the fact that there is a pair of variables for each
tetrahedron can be viewed as a consequence of an SO(4)-valued parallel
transport along the edges dual to the tetrahedra. We reconstruct the parallel
transport of which only the action of SO(4) on S^3 is physically relevant and
rewrite the Barrett-Crane model as an SO(4) lattice BF-theory living on the
2-complex dual to the triangulation subject to suitable constraints whose form
we derive at the quantum level. Our reformulation of the Barrett-Crane model in
terms of continuous variables is suitable for the application of various
analytical and numerical techniques familiar from Statistical Mechanics.Comment: 33 pages, LaTeX, combined PiCTeX/postscript figures, v2: note added,
TeX error correcte
Area dependence of interlayer tunneling in strongly correlated bilayer two-dimensional electron systems at ν_T = 1
The area and perimeter dependence of the Josephson-like interlayer tunneling signature of the coherent ν_T = 1 quantum Hall phase in bilayer two-dimensional electron systems is examined. Electrostatic top gates of various sizes and shapes are used to locally define distinct ν_T = 1 regions in the same sample. Near the phase boundary with the incoherent ν_T = 1 state at large layer separation, our results demonstrate that the tunneling conductance in the coherent phase is closely proportional to the total area of the tunneling region. This implies that tunneling at ν_T = 1 is a bulk phenomenon in this regime
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
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