187 research outputs found
A matrix solution to pentagon equation with anticommuting variables
We construct a solution to pentagon equation with anticommuting variables
living on two-dimensional faces of tetrahedra. In this solution, matrix
coordinates are ascribed to tetrahedron vertices. As matrix multiplication is
noncommutative, this provides a "more quantum" topological field theory than in
our previous works
Polyhedra in loop quantum gravity
Interwiners are the building blocks of spin-network states. The space of
intertwiners is the quantization of a classical symplectic manifold introduced
by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to
interpret generic configurations in this space as bounded convex polyhedra in
Euclidean space: a polyhedron is uniquely described by the areas and normals to
its faces. We provide a reconstruction of the geometry of the polyhedron: we
give formulas for the edge lengths, the volume and the adjacency of its faces.
At the quantum level, this correspondence allows us to identify an intertwiner
with the state of a quantum polyhedron, thus generalizing the notion of quantum
tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent
intertwiners result to be peaked on the classical geometry of polyhedra. We
discuss the relevance of this result for loop quantum gravity. In particular,
coherent spin-network states with nodes of arbitrary valence represent a
collection of semiclassical polyhedra. Furthermore, we introduce an operator
that measures the volume of a quantum polyhedron and examine its relation with
the standard volume operator of loop quantum gravity. We also comment on the
semiclassical limit of spinfoams with non-simplicial graphs.Comment: 32 pages, many figures. v2 minor correction
Spin Foam Diagrammatics and Topological Invariance
We provide a simple proof of the topological invariance of the Turaev-Viro
model (corresponding to simplicial 3d pure Euclidean gravity with cosmological
constant) by means of a novel diagrammatic formulation of the state sum models
for quantum BF-theories. Moreover, we prove the invariance under more general
conditions allowing the state sum to be defined on arbitrary cellular
decompositions of the underlying manifold. Invariance is governed by a set of
identities corresponding to local gluing and rearrangement of cells in the
complex. Due to the fully algebraic nature of these identities our results
extend to a vast class of quantum groups. The techniques introduced here could
be relevant for investigating the scaling properties of non-topological state
sums, being proposed as models of quantum gravity in 4d, under refinement of
the cellular decomposition.Comment: 20 pages, latex with AMS macros and eps figure
The influence of the cosmological expansion on local systems
Following renewed interest, the problem of whether the cosmological expansion
affects the dynamics of local systems is reconsidered. The cosmological
correction to the equations of motion in the locally inertial Fermi normal
frame (the relevant frame for astronomical observations) is computed. The
evolution equations for the cosmological perturbation of the two--body problem
are solved in this frame. The effect on the orbit is insignificant as are the
effects on the galactic and galactic--cluster scales.Comment: To appear in the Astrophysical Journal, Late
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Quantum geometry with intrinsic local causality
The space of states and operators for a large class of background independent
theories of quantum spacetime dynamics is defined. The SU(2) spin networks of
quantum general relativity are replaced by labelled compact two-dimensional
surfaces. The space of states of the theory is the direct sum of the spaces of
invariant tensors of a quantum group G_q over all compact (finite genus)
oriented 2-surfaces. The dynamics is background independent and locally causal.
The dynamics constructs histories with discrete features of spacetime geometry
such as causal structure and multifingered time. For SU(2) the theory satisfies
the Bekenstein bound and the holographic hypothesis is recast in this
formalism.Comment: Latex 33 pages, 7 Figure, epsfi
Search for Specific Biomarkers of IFNβ Bioactivity in Patients with Multiple Sclerosis
Myxovirus A (MxA), a protein encoded by the MX1 gene with antiviral activity, has proven to be a sensitive measure of IFNβ bioactivity in multiple sclerosis (MS). However, the use of MxA as a biomarker of IFNβ bioactivity has been criticized for the lack of evidence of its role on disease pathogenesis and the clinical response to IFNβ. Here, we aimed to identify specific biomarkers of IFNβ bioactivity in order to compare their gene expression induction by type I IFNs with the MxA, and to investigate their potential role in MS pathogenesis. Gene expression microarrays were performed in PBMC from MS patients who developed neutralizing antibodies (NAB) to IFNβ at 12 and/or 24 months of treatment and patients who remained NAB negative. Nine genes followed patterns in gene expression over time similar to the MX1, which was considered the gold standard gene, and were selected for further experiments: IFI6, IFI27, IFI44L, IFIT1, HERC5, LY6E, RSAD2, SIGLEC1, and USP18. In vitro experiments in PBMC from healthy controls revealed specific induction of selected biomarkers by IFNβ but not IFNγ, and several markers, in particular USP18 and HERC5, were shown to be significantly induced at lower IFNβ concentrations and more selective than the MX1 as biomarkers of IFNβ bioactivity. In addition, USP18 expression was deficient in MS patients compared with healthy controls (p = 0.0004). We propose specific biomarkers that may be considered in addition to the MxA to evaluate IFNβ bioactivity, and to further explore their implication in MS pathogenesis
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