Q-deformed spin foam models of quantum gravity

In summary: You might be interested in Dan Chritensen's home page, if you haven't visited.He has a big list of useful links to LQG-related information.With his specialty in computing he also has some nice computer graphics, or did the last time I went there
  • #1

jal

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For those who have been following my model, I see this as another step in the right direction.
http://arxiv.org/pdf/0704.0278
q-deformed spin foam models of quantum gravity
Igor Khavkine and J. Daniel Christensen
02 April 2007
Large triangulations are necessary to approximate semiclassical space-times. The possibility of obtaining numerical results from larger triangulations takes us one step closer to that goal and increases the number of facets from which the physical properties of a spin foam model may be examined. As an example, we are able to study how the spin-spin correlation varies with the distance between faces in the triangulation.

Consider a triangulated 4-manifold. Let _n denote the set of n-dimensional simplices of the triangulation. The dual 2-skeleton is formed by associating a dual vertex, edge and polygonal face to each 4-simplex, tetrahedron, and triangle of the triangulation, respectively.
Given the discrete structure of our spacetime model, it is conceivable that this combinatorial distance, multiplied by a fundamental unit of length, approximates some notion of distance derived from the dynamical geometry of the spin foam model.
(I use a double tetra. See my visuals)
jal
 
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  • #2
You might be interested in Dan Chritensen's home page, if you haven't visited.

He has a big list of useful links to LQG-related information.
With his specialty in computing he also has some nice computer graphics, or did the last time I went there

http://jdc.math.uwo.ca/

"...I am an associate professor in the Department of Mathematics at The University of Western Ontario in London, Ontario, with a cross appointment to the Department of Applied Mathematics, and an affiliation with the Perimeter Institute for Theoretical Physics.

I enjoy hiking, rock climbing, kayaking and other outdoors sports. Here are photos from some trips I have been on.

Contact information is below..."

Here is his
Information on spin foam models of quantum gravity
(earlier title was: Spin networks, spin foams and loop quantum gravity)
http://jdc.math.uwo.ca/spin-foams/index.html (need to scroll down to find the URLs)

Their supercomputer is a Beowolf cluster.

the QG group at Western (also known as UWO) consists of 4 researchers

Dan
a postdoc named Josh Willis
two PhD students named Igor Khavkine and Wade Cherrington.
and I think they will have a fifth person soon (a PhD student of John Baez who is finishing thesis now and will move up there)

Christensen has co-authored 3 papers with John Baez.

Western seems like a good place for QG these days.
 
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  • #3
Well Marcus… you have made my day.
I have never thought that the path that I was following was untrodded.
Lo and behold up in the distance is a figure.
http://jdc.math.uwo.ca/
Dan Christensen's home page
http://jdc.math.uwo.ca/spin-foams/index.html
Spin networks, spin foams and loop quantum gravity
http://gregegan.customer.netspace.net.au/SiteMap.html#d16_4_1

http://gregegan.customer.netspace.net.au/SCHILD/Spin/SN.html
Spin Networks
http://gregegan.customer.netspace.net.au/SCHILD/Spin/Spin.html
The applet below displays a small spin network

Perhaps, he has missed observing some of the interesting points along the path, (a fundamental unit of length).
I shall hurry forward and ask for an audience.
Perhaps, he might be able to get “gregegan” to make a dynamic visual of my double tetra.

jal
 

1. What is a Q-deformed spin foam model of quantum gravity?

A Q-deformed spin foam model is a mathematical framework used to describe the quantum properties of spacetime, specifically in the context of quantum gravity. It is based on the concept of spin foam, which represents the geometry of spacetime as a network of interconnected triangles. The "Q-deformation" refers to the use of a mathematical tool called a quantum group, which introduces a new parameter into the model and allows for a more flexible description of spacetime.

2. How is a Q-deformed spin foam model different from other models of quantum gravity?

Unlike other models of quantum gravity, which often focus on a discrete or continuous description of spacetime, a Q-deformed spin foam model combines both approaches by using discrete spin foam structures to describe the geometry of continuous spacetime. This allows for a more granular understanding of quantum spacetime and its dynamics.

3. What are the advantages of using a Q-deformed spin foam model?

One of the main advantages of using a Q-deformed spin foam model is its ability to incorporate both discrete and continuous aspects of spacetime. This allows for a more comprehensive understanding of the quantum nature of spacetime and its dynamics. Additionally, the use of quantum groups allows for a more flexible and robust mathematical framework compared to other models.

4. What are the potential applications of Q-deformed spin foam models?

Q-deformed spin foam models have potential applications in the field of quantum gravity, specifically in understanding the dynamics of spacetime at the smallest scales. They can also be used to investigate the nature of black holes and the early universe, as well as provide insights into the unification of quantum mechanics and general relativity.

5. What are the current challenges and limitations of Q-deformed spin foam models?

One of the main challenges of Q-deformed spin foam models is their complexity, both in terms of mathematical formulation and computational requirements. This makes it difficult to test and validate these models against experimental data. Additionally, the use of quantum groups introduces additional parameters that need to be constrained, which can be a limitation in terms of predictive power.

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