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

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Discussion Overview

The discussion revolves around the concept of boundaries in spinfoams and spin networks within Loop Quantum Gravity (LQG) theory. Participants explore definitions, relationships between bulk and boundary, and the significance of these boundaries in the context of LQG.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the boundary of a spinfoam is indeed a spin network and seeks definitions for boundaries in both spinfoams and spin networks.
  • Another participant suggests consulting a specific book that discusses classical discretization of General Relativity and the connection between bulk and boundary, particularly in the context of 3D and 4D spacetime.
  • A third participant references a research paper that defines the notion of a boundary and discusses the spin network basis for the boundary Hilbert space.
  • One participant proposes that in a spin network, a boundary consists of a minimal set of edges that connect two vertices, provided there is no alternative path that avoids these edges.
  • There are technical issues noted regarding the accessibility of the book's draft version, with participants discussing the functionality of the provided link.

Areas of Agreement / Disagreement

Participants express varying interpretations of what constitutes a boundary in spinfoams and spin networks, indicating that multiple competing views remain. The discussion does not reach a consensus on definitions or the nature of boundaries.

Contextual Notes

Some definitions and assumptions regarding boundaries in spinfoams and spin networks remain unresolved, and there are references to specific sections in literature that may clarify these concepts further.

naima
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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
 
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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
 
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.
 
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?
 
naima said:
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.
 

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