Understanding the Boundary of a Spinfoam and Spin Network in LQG Theory

[naima]

I read in wikipedia that the boundary of a spinfoam is a spin network.
Is it true?
How can we define what is the boundary of a finite connected spinfoam?
I have the same question for a spin network.
As in LQG boundaries are of paramount importance, I think that we have to define them.
Thanks

 

[julian]

You could look at the book "Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory" There is a chapter on classical discretization of GR. You may want to look particularly at section 4.4 where they start with the simple case of 3-spatial dimensions and define the connection between bulk and boundary and establish notation. At the start of chapter 7 they talk about the generalization to 4D spacetime.

A draft version of the book is quoted as here http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf

 

[atyy]

http://arxiv.org/abs/1209.4539
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Bianca Dittrich, Frank Hellmann, Wojciech Kaminski

The notion of a boundary is defined in section 3.1, and the spin network basis for the boundary Hilbert space is given in section 3.2.

 

[naima]

At the start of chapter 7 they talk about the generalization to 4D spacetime.

A draft version of the book is quoted as here http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf

there
is a problem with the link

 

[naima]

As i understand it in a spin network a boundary is a minimal set of edges. a bondary js between two vertices
if there is no path between them which can avoid these edges. Is this correct?

 

[marcus]

there
is a problem with the link

Try again, I think it is OK now.
It takes a couple of minutes to download the complete draft of the book (illustrations etc.) so it is not fast, but it does work.