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Q-deformed spin foam models of quantum gravity
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Apr4-07, 10:47 AM
For those who have been following my model, I see this as another step in the right direction.
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)
Apr4-07, 11:32 AM
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
"...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
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.
Apr4-07, 12:55 PM
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.
Dan Christensen's home page
Spin networks, spin foams and loop quantum gravity
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.
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