A Retrieving the loops on spinfoams

[Heidi]

I am looking for a paper i read several yeais ago.
is was on a graphical way to see all the closed loops associated to an oriented spinfoam. there was a set of lines on each edge.
do you see what i mean?
thanks

 

[Paul Colby]

Any chance https://arxiv.org/abs/2102.05881 was the paper, or should I keep guessing?

 

[Heidi]

It was more simple that this paper. more like a trick than a theory...
with an author like smolin or rovelli (maybe).

 

[Paul Colby]

You really should try to find the paper and post the link. Others might be interested.

 

[Heidi]

what i remember is that in finite connected spinfoam if you are on an edge and follow a random outgoing edge when you meet a node you will follow a closed path ending on the startind edge. this is a loop that you can draw near the edges. other choices would give over loopq and over drawings.
so you get for each edge parrallel different loop lines.
Draw the Mercedes cirle with 3 segments , choose orientations for the edges (at less one ingoing and one outgoing one each nodes) and see the loops ...

 

[Heidi]

I found this interesting paper
SPIN NETWORKS AND THE BRACKET POLYNOMIAL
https://homepages.math.uic.edu/~kauffman/spinnet.pdf
it gives the identities of the binor calcus based on the properties of the epsilon tensor. this epsilon tensor appears in the LQG intertwiners.

 

[Paul Colby]

Louis H. Kauffman wrote a book ”Knots and Physics” which might be of interest as it provides a more in depth introduction to the mathematic. I go through phases on things like this. Never quite clear on how much of it is really physics.

 

[Heidi]

Hi Paul,
there is something that bothers me.
Links in LQG have orientations so a node can have only ingoing links.
But consider the loops in the recoupling theory. we have strands associated with links
ie if a link has a j spin we find 2j lines in the strand. if they correspond to loops they should
have an orientation. How to manage these orientations? what if such a loop goes thru the node with only ingoing links?

 

[Paul Colby]

Sorry, I haven’t looked at LQG closely enough to even guess. Several years ago I did attempt a reading of a paper that approached QED from a loop approach similar to LQG. My hope was to gain insight by looking at how a theory I partially understand is handled.

BTW I took another swing at “Knots and Physics”. It’s quite readable.

 

[Heidi]

Do you have access to Rovelli's book (quantum gravitaty)?
threr are draft pdf versions
https://www.cpt.univ-mrs.fr/~rovelli/book.pdf
it would be easier to cite formulas of the book or sentences

 

[Paul Colby]

Haven’t looked at it. I’m probably ripe for another LQG attempt. Thanks for the link.

 

[Heidi]

When i opened this thread , i had in mind what Rovelli wrote in in the 6.3.2 paragraph.(details on the spin networks)
see how from a simple spin network he obtains the corresponding loop states
the remainig problem for me is the orientation of the loops.