11,137 research outputs found
Some Considerations on Discrete Quantum Gravity
Recent results in Local Regge Calculus are confronted with Spin Foam
Formalism. Introducing Barrett-Crane Quantization in Local Regge Calculus makes
it possible to associate a unique Spin with an hinge , fulfilling
one of the requirements of Spin Foam definition. It is shown that inter-twiner
terms of Spin Foam can follow from the closure constraint in Local Regge
Calculus.
Dedicated to Beppe Marmo for his 65th BirthdayComment: 7 pages, FunInGeo Conference proceedings, Ischia-Italy, 08-12 June
2011; accepted for publication in the International Journal of Geometric
Methods in Modern Physic
From Local Regge Calculus towards Spin Foam Formalism?
We introduce the basic elements of SO(n)-local theory of Regge Calculus. A
first order formalism, in the sense of Palatini, is defined on the metric-dual
Voronoi complex of a simplicial complex. The Quantum Measure exhibits an
expansion, in four dimensions, in characters of irreducible representation of
SO(4) which has close resemblance and differences as well with the Spin Foam
Formalism. The coupling with fermionic matter is easily introduced which could
have consequences for the Spin Foam Formalism and Loop Quantum Gravity.Comment: 14 pages, 1 figures, proceeding of the Albert Einstein's
International Conference 18-22 July 200
The Orlicz version of the Minkowski problem on for
An Orlicz version of the -Minkowski problem on is discussed
corresponding to the case
Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms
We propose strongly consistent algorithms for reconstructing the
characteristic function 1_K of an unknown convex body K in R^n from possibly
noisy measurements of the modulus of its Fourier transform \hat{1_K}. This
represents a complete theoretical solution to the Phase Retrieval Problem for
characteristic functions of convex bodies. The approach is via the closely
related problem of reconstructing K from noisy measurements of its covariogram,
the function giving the volume of the intersection of K with its translates. In
the many known situations in which the covariogram determines a convex body, up
to reflection in the origin and when the position of the body is fixed, our
algorithms use O(k^n) noisy covariogram measurements to construct a convex
polytope P_k that approximates K or its reflection -K in the origin. (By recent
uniqueness results, this applies to all planar convex bodies, all
three-dimensional convex polytopes, and all symmetric and most (in the sense of
Baire category) arbitrary convex bodies in all dimensions.) Two methods are
provided, and both are shown to be strongly consistent, in the sense that,
almost surely, the minimum of the Hausdorff distance between P_k and K or -K
tends to zero as k tends to infinity.Comment: Version accepted on the Journal of the American Mathematical Society.
With respect to version 1 the noise model has been greatly extended and an
appendix has been added, with a discussion of rates of convergence and
implementation issues. 56 pages, 4 figure
String duality transformations in gravity from Noether symmetry approach
We select gravity models that undergo scale factor duality
transformations. As a starting point, we consider the tree-level effective
gravitational action of bosonic String Theory coupled with the dilaton field.
This theory inherits the Busher's duality of its parent String Theory. Using
conformal transformations of the metric tensor, it is possible to map the
tree-level dilaton-graviton string effective action into gravity,
relating the dilaton field to the Ricci scalar curvature. Furthermore, the
duality can be framed under the standard of Noether symmetries and exact
cosmological solutions are derived. Using suitable changes of variables, the
string-based Lagrangians are shown in cases where the duality
transformation becomes a parity inversion.Comment: v1: 13 pages; v2: minor rephrasings, published versio
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