# QFT with curved spacetime

1. Mar 31, 2005

### misogynisticfeminist

I was wondering, is there a possibillity that QFT with curved spacetime is a the path to unification? Also, what advances are there in constructing QFTs with dynamic spacetime? If this way is feasible, who are the people spearheading it?

Last edited: Mar 31, 2005
2. Mar 31, 2005

### marcus

there is a widely shared hunch among Loop Quantum Gravity people that QFT should be constructed on a QUANTUM-dynamic spacetime, because it hasnt worked to construct it on non-quantum, or classical, dynamic spacetime.

the classical, unquantized, version of dynamic spacetime is called General Relativity, it was proposed in 1915.
So far no one has been able to construct QFT on the dynamic spacetime of Gen Rel.
QFT has been constructed only on rigid (flat or curved) spaces whose geometry is not dynamic but is fixed ahead of time.

so the intuition driving the LQG effort is that if we can just get a quantum theory of spacetime (a quantum version of Gen Rel) then it will be possible to build a QFT on it

First get the spacetime right, they say, then add matter to the picture.

when you here about current progress in LQG, it is important to remember that what they are developing is exactly this: a quantum theory of dynamical spacetime geometry

(Gen Rel says that gravity is geometry, in the way spacetime is curved, and so a quantum gravity theory must be a quantum geometry theory----this is the LQG point of view, so that is the approach they take)

other people may try to represent the "force" of gravity in context of rigid space, for instance in flat space. this is yet another approach, probably some other poster would like to tell you about that approach

Last edited: Mar 31, 2005
3. Mar 31, 2005

Staff Emeritus
Marcus, the idea of QFT in curved spacetime is not about rigid spacetime but about mating QFT to GR with its dynaminc spacetime. There are many problems with this, such as the instability of spinors under general diffeomorphisms and the apparent unrenormalizabilty of this meld in its perturbative form, which given that neither QFT nor GR are really known non-perturbatively, would seem to be a killer. But work goes on, and don't forget the Schroedenger-Einstein nonsymmetric theory! I'll bet Shiflett is trying to quantize that right now!

4. Mar 31, 2005

### marcus

it is at the stage of constructing the quantum dynamic spacetime
(which you must do first before putting on matter)
the people spearheading are Martin Bojowald, Laurent Freidel, Lee Smolin, Carlo Rovelli, Abhay Ashtekar, Thomas Thiemann, Rodolfo Gambini, Renate Loll, and their students and colleagues that write papers with them. You can generate a list by doing a search at arxiv.org for papers by these people and seeing who has co-authored with them.

Some, like Bojowald and Freidel in separate efforts, have started putting matter-fields in the picture.

5. Mar 31, 2005

### marcus

thanks for the correction. Glad someone else is helping answer. I was confusing this with something Haelfix said about picking out a set of interesting curved geometries and constructing string theory case by case on curved (but rigid) geometries. maybe that is done too.

I am delighted to know that people are trying to mate QFT to GR with its dynamic spacetime!

so I guess I would like to subscribe to misogynist's question: who are the people spearheading it?

Last edited: Mar 31, 2005
6. Mar 31, 2005

Staff Emeritus
Marcus, the idea of QFT in curved spacetime is not about rigid spacetime but about mating QFT to GR with its dynaminc spacetime. There are many problems with this, such as the instability of spinors under general diffeomorphisms and the apparent unrenormalizabilty of this meld in its perturbative form, which given that neither QFT nor GR are really known non-perturbatively, would seem to be a killer. But work goes on, and don't forget the Schroedenger-Einstein nonsymmetric theory! I'll bet Shiflett is trying to quantize that right now!

7. Mar 31, 2005