From TheBestLinks.com
A spin network is a graph whose edges are associated with representations of a Lie group, G and vertices are associated with intertwiners of the edge reps adjacent to it. It was invented by Roger Penrose in 1971. Spin networks were applied to the physics problem of quantum gravity by Carlo Rovelli, Lee Smolin, Fotini Markopoulou-Kalamara, and others to reformulate loop quantum gravity and gauge theory.
One of the key results of loop quantum gravity is quantization of areas:
according to several related derivations based on loop quantum gravity,
the operator of the area <math>A<math> of a two-dimensional surface
<math>\Sigma<math> should have discrete spectrum. Every spin network is an eigenstate of each such operator, and the area
eigenvalue equals
- <math>A_{\Sigma} = 8\pi G_{\mathrm{Newton}} \gamma
\sum_i \sqrt{j_i(j_i+1)}<math>
where the sum goes over all intersections <math>i<math> of
<math>\Sigma<math> with the spin network. In this formula,
<math>G_{\mathrm{Newton}}<math> is the gravitational constant,
<math>\gamma<math> is the Immirzi parameter and
<math>j_i=0,0.5,1,1.5,\dots<math> is the spin associated with the
link <math>i<math> of the spin network. The two-dimensional area is
therefore "concentrated" in the intersections with the spin network.
Similar quantization applies to the volume operators but mathematics
behind these derivations is less convincing.
Related links
Top visited
0 of
0 links
[no links posted yet]
>> place link >>
Discussion
Last posted
0 of
0 messages
[no messages posted yet]
>> post message >>
Watch
You can
add this article to your own "watchlist" and receive e-mail notification about all changes in this page.
