15,983 research outputs found
The group inverse of subdivision networks
In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.Peer ReviewedPostprint (author's final draft
Effective resistances and Kirchhoff index in subdivision networks
We define a subdivision network ¿S of a given network ¿; by inserting a new vertex in every edge, so that each edge is replaced by two new edges with conductances that fulfill electrical conditions on the new network. In this work, we firstly obtain an expression for the Green kernel of the subdivision network in terms of the Green kernel of the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the subdivision network in terms of the corresponding parameters on the base network. Finally, as an example, we carry out the computations in the case of a wheel.Peer ReviewedPostprint (author's final draft
On knottings in the physical Hilbert space of LQG as given by the EPRL model
We consider the EPRL spin foam amplitude for arbitrary embedded
two-complexes. Choosing a definition of the face- and edge amplitudes which
lead to spin foam amplitudes invariant under trivial subdivisions, we
investigate invariance properties of the amplitude under consistent
deformations, which are deformations of the embedded two-complex where faces
are allowed to pass through each other in a controlled way. Using this
surprising invariance, we are able to show that in the physical Hilbert space
as defined by the sum over all spin foams contains no knotting classes of
graphs anymore.Comment: 22 pages, 14 figure
Holonomy Spin Foam Models: Definition and Coarse Graining
We propose a new holonomy formulation for spin foams, which naturally extends
the theory space of lattice gauge theories. This allows current spin foam
models to be defined on arbitrary two-complexes as well as to generalize
current spin foam models to arbitrary, in particular finite groups. The
similarity with standard lattice gauge theories allows to apply standard coarse
graining methods, which for finite groups can now be easily considered
numerically. We will summarize other holonomy and spin network formulations of
spin foams and group field theories and explain how the different
representations arise through variable transformations in the partition
function. A companion paper will provide a description of boundary Hilbert
spaces as well as a canonical dynamic encoded in transfer operators.Comment: 36 pages, 12 figure
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