446 research outputs found
Locality and Translations in Braided Ribbon Networks
An overview of microlocality in braided ribbon networks is presented.
Following this, a series of definitions are presented to explore the concept of
microlocality and the topology of ribbon networks. Isolated substructure of
ribbon networks are introduced, and a theorem is proven that allows them to be
relocated. This is followed by a demonstration of microlocal translations.
Additionally, an investigation into macrolocality and the implications of
invariants in braided ribbon networks are presented.Comment: 12 pages, 12 figure
Numerical simulation of mesomechanical behavior of porous brittle materials
The influence of the types of porous structure on the features of deformation, damage accumulation and fracture of mesovolumes of brittle materials is studied. At the mesoscale, the pores of different shape are taken into account explicitly. The digital models were made using random values of coordinates and radii of spherical voids or solid spheres. For numerical modeling of the mechanical behavior up to failure, the evolutionary approach is applied with considering the nonlinear constitutive equations to describe damage accumulation and its influence on the degradation of the strength properties of the frame of porous ceramics. The calculated averaged stress-strain diagrams were shown to be sensitive not only to the value of porosity but also to the shape of pores. The simulation results are validated with experimental data for zirconia and alumina ceramics. Good qualitative and quantitative agreement of modeling results with experimental data suggests that taking into account of two-scale porosity in the form of explicit consideration of large pores at the mesoscale and implicit integrated consideration of tiny pores and cracks from the microscale in the form of accumulated damage is quite sufficient in the framework of the hierarchical modeling
Fractal Structure of Loop Quantum Gravity
In this paper we have calculated the spectral dimension of loop quantum
gravity (LQG) using simple arguments coming from the area spectrum at different
length scales. We have obtained that the spectral dimension of the spatial
section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar
field decrees from high to low energy. We have calculated the spectral
dimension of the space-time also using results from spin-foam models, obtaining
a 2-dimensional effective manifold at hight energy. Our result is consistent
with other two approach to non perturbative quantum gravity: causal dynamical
triangulation and asymptotic safety quantum gravity.Comment: 5 pages, 5 figure
Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
Loop Quantum Gravity defines the quantum states of space geometry as spin
networks and describes their evolution in time. We reformulate spin networks in
terms of harmonic oscillators and show how the holographic degrees of freedom
of the theory are described as matrix models. This allow us to make a link with
non-commutative geometry and to look at the issue of the semi-classical limit
of LQG from a new perspective. This work is thought as part of a bigger project
of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure
On the diffeomorphism commutators of lattice quantum gravity
We show that the algebra of discretized spatial diffeomorphism constraints in
Hamiltonian lattice quantum gravity closes without anomalies in the limit of
small lattice spacing. The result holds for arbitrary factor-ordering and for a
variety of different discretizations of the continuum constraints, and thus
generalizes an earlier calculation by Renteln.Comment: 16 pages, Te
Quantum gravity and the standard model
We show that a class of background independent models of quantum spacetime
have local excitations that can be mapped to the first generation fermions of
the standard model of particle physics. These states propagate coherently as
they can be shown to be noiseless subsystems of the microscopic quantum
dynamics. These are identified in terms of certain patterns of braiding of
graphs, thus giving a quantum gravitational foundation for the topological
preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space
has a basis of states given by ribbon graphs embedded in a three-dimensional
manifold up to diffeomorphisms, and the dynamics is given by local moves on the
graphs, such as arise in the representation theory of quantum groups. For such
models, matter appears to be already included in the microscopic kinematics and
dynamics.Comment: 12 pages, 21 figures, improved presentation, results unchange
Free vacuum for loop quantum gravity
We linearize extended ADM-gravity around the flat torus, and use the
associated Fock vacuum to construct a state that could play the role of a free
vacuum in loop quantum gravity. The state we obtain is an element of the
gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a
natural consequence of the momentum cutoff of the original Fock state. It has
the form of a Gaussian superposition of spin networks. We show that the peak of
the Gaussian lies at weave-like states and derive a relation between the
coloring of the weaves and the cutoff scale. Our analysis indicates that the
peak weaves become independent of the cutoff length when the latter is much
smaller than the Planck length. By the same method, we also construct
multiple-graviton states. We discuss the possible use of these states for
deriving a perturbation series in loop quantum gravity.Comment: 30 pages, 3 diagrams, treatment of phase factor adde
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