What Does Quantum Gravity Scattering Amplitudes Mean?

[inflector]

What Does "Quantum Gravity Scattering Amplitudes" Mean?

I've seen it referenced in a few papers but I can't seem to find a definition.

I know what "scattering amplitudes" means but don't understand the relationship with quantum gravity.

What precisely is doing the scattering in quantum gravity?

 

[marcus]

I've seen it referenced in a few papers but I can't seem to find a definition.

I know what "scattering amplitudes" means but don't understand the relationship with quantum gravity.

What precisely is doing the scattering in quantum gravity?

In matterless LQG that would have to refer to the scattering of gravitons by gravitons.

So-called "n-point functions"

It is challenging to derive even the propagator of a single graviton in LQG.

A particle is an idealization primarily applicable to flat geometry (or some other convenient fixed geometry). Particles are a great way to treat fields in an approximately flat geometry.
So how do you even have particles in a background independent theory like spinfoam LQG?
The answer is that you nail down the boundary of the spinfoam to force it to be approximately flat. Flat in a 4D sense, like the space of special relativity---the way geometry would be if gravity was turned off and there was no curvature.

So back around 2007 Rovelli did this. He and co-workers considered spinfoams with boundary, and restricted the boundary to be flat, and forced the spinfoam to emulate a nearly flat 4D world, and so then gravitons were available. And they studied the LQG graviton propagator.

The next step should be to study two gravitons, interacting or scattering. I don't know how that stands at the moment. There is a lot of work to do, in the program, and I think at most a dozen people who could address this particular issue. Maybe there will be a status report given at Loops 2011.

If someone knows more, please correct me on this. Maybe I can find a paper that talks about LQG graviton scattering amplitudes. I'll look.

 

[inflector]

Okay, so I was right about scattering requiring particles at least.

I didn't know that LQG, like string theory, requires/uses gravitons. I'm not sure I buy the idea of gravitons necessarily at this point, but at least I know what LQG is assuming.

Thank you.

 

[marcus]

Okay, so I was right about scattering requiring particles at least.

I didn't know that LQG, like string theory, requires/uses gravitons. I'm not sure I buy the idea of gravitons necessarily at this point, but at least I know what LQG is assuming.
...

LQG doesn't require gravitons, as I think you had already gathered. We can think of graviton as a mathematical tool. an idealization that works very well in certain limited nearly flat situations. It is not a useful idea in highly curved dynamically changing geometry.

The real thing is the field. Sometimes it is useful to view the field as nearly flat but with small ripples on it. Gravitons exist when we find it convenient for them to exist.

Rovelli et al did not HAVE to investigate how gravitons act in LQG. But they did, partly because it is a way of proving that NEWTON'S INVERSE SQUARE law holds in LQG. The graviton propagator should fall of as the square of distance. And good news! It turns out that it does hold.

I guess you could say that the LQG graviton papers were part of a strategy to get hands on the flat limit of LQG.

In case anyone wants to find the graviton propagator papers one way is to go to arxiv.org and press search, and get:
http://arxiv.org/multi?group=grp_physics&/find=Search
and type in rovelli, and get
http://arxiv.org/find/grp_physics/1/au:+rovelli/0/1/0/all/0/1
and go back to 2006 or 2007
but there are better ways obviously, title, keyword...

Here's one from 2007
http://arxiv.org/abs/0711.1284
It probably has references to some earlier work.
I think there is a solo paper by somebody else in the group, but I forget who.

 

[inflector]

LQG doesn't require gravitons, as I think you had already gathered. We can think of graviton as a mathematical tool. an idealization that works very well in certain limited nearly flat situations. It is not a useful idea in highly curved dynamically changing geometry.

Ah, well that is what I originally thought.

Rovelli et al did not HAVE to investigate how gravitons act in LQG. But they did, partly because it is a way of proving that NEWTON'S INVERSE SQUARE law holds in LQG. The graviton propagator should fall of as the square of distance. And good news! It turns out that it does hold.

I guess you could say that the LQG graviton papers were part of a strategy to get hands on the flat limit of LQG.

Makes sense. Thanks for the clarification and links.