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**Seething expanding geometry--new LQG view of reality**

A view of reality emerging from current LQG research (like 1004.1780) is somewhat analogous to the "seething vacuum" of quantum field theory. But it is a "seething geometry" in which bits of area and volume constantly come into existence and go out of existence.

I suppose that eventually the LQG geometry will seethe and boil not only with bits area and volume but also with matter. In other words, some elaboration of the math will be found so that particle fields living in the geometry can properly be added to the picture. (Several ways to do that have already been proposed, but it's still early days.)

The formalism uses a more complicated version of Feynman diagrams. A spin network is an instantaneous state of geometry: the nodes represent bits of volume and the links represent bits of area.

**Nodes and links**are items which an observable---an operator measuring the volume of some physical region or the area of some physical surface---might or might not detect.

A spin foam is the history or "track" of a spin network as it evolves in time. To keep the terminology straight, different words are used to describe spin foams:

**vertex, edge, face**. As a spin network evolves in time, its nodes describe edges, and its links describe faces. Geometric events (creation annihilation of some geometric element) occur at the vertices of the spin foam.

It is not hard to keep these few terms straight and it helps to use them consistently. Node and link (volume and area) at the instantaneous geometry level. Vertex, edge, face at the level of evolving geometry---the histories of a "sum over histories".

Because the spinfoam vertex is so critical---it is where important stuff like creation annihilation happens---the vertex amplitude practically defines the theory. The idea is that, amplitude being a complex number akin to probability, if you want to know the amplitude of evolving from geometry A to geometry B, you consider all the possible spinfoam diagrams that can get you from A to B and add up their amplitudes. The amplitude of each individual spin foam is the total amplitude of its parts (primarily the vertices.) So the vertex formula plays a key role in determining the dynamics of evolving geometry.

The "new Lqg" paper I mentioned ( http://arxiv.org/abs/1004.1780 ) gives rules to calculate these amplitudes for "geometry's Feynman diagrams." They aren't the only proposed rules--the situation is still being sorted out. Alternative ways of calculating amplitudes, which increasingly seem to give the same answers, are discussed in the paper.

There is a lot happening around this new version of LQG so it makes sense to have a thread to watch the proceedings. This week Rovelli will be teaching a minicourse on it at the Morelia QG school. The week after, starting 4 July there will be the triennial GR conference. Rovelli and others will be talking there. The April paper already has more citations than any other QG paper from the second quarter of 2010. So it seems reasonable to expect a research thrust along these lines.

The three main QG research areas I am personally most interested in watching are LQG, NCG, and EFT. NCG here means work by Connes and by Marcolli and her associates. EFT has become interesting because it appears that a UV fixed point exists (asymptotic safety) so that effective field theory of various types may afford a valid approach. Of these three (LQG, NCG and EFT) it seems that LQG is of particular interest because it proposes to identify microscopic geometric degrees of freedom.

The nature of these microgeometric degrees of freedom, if correctly identified, could help to explain

**why**geometry enjoys the asymptotic safety of a UV fixed point.

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