I Spin Foam models in Loop Quantum Gravity

[asimov42]

Hi all,

I fairly basic question about spin foam models in loop quantum gravity. I just want to verify that spin foams represent effectively represent all of spacetime (in a quantum form), and that the idea is that general relativity can be obtained in the classical limit? Not sure if that's correct?

 

[asimov42]

Also, what does is mean, roughly, for time to be absent in LQG theories - isn't time required to recover relativity? (I believe this is known as the "problem of time')

 

[atyy]

Spin foams are like Feynman diagrams, which represent steps used to calculate a quantity called the "transition amplitude" that is used in normal quantum mechanics (ie. not quantum gravity) to calculate the probability of transitioning in time from state A to state B.

Regarding "time" in spin foams, Jonathan Engle says in his review "It is clear, therefore, that in quantum gravity one cannot interpret the Feynman path integral in terms of time evolution, as was done in (4). In fact, the interpretation is dierent. Instead, in the interpretation of the path integral, the time evolution map is replaced by a projector P onto [solutions of the Hamilton constraint]." https://arxiv.org/abs/1303.4636 (p9)

I think the hope is that general relativity can be obtained in the classical limit, but I don't think that has yet been shown. Nor whether the theory is a consistent quantum theory.

 

[julian]

Indeed the Hamiltonian constraint generates time gauge transformations and solving it is solving a gauge transformation equation.

Physical meaning to transition amplitudes and time evolution however can be obtained, when it comes to background independent scattering amplitudes for example.

There the idea is to study the boundary amplitude, namely a path integral over a finite space-time region, seen as a function of the boundary value of the field, peaked on a semi-classical state which, of course, includes the gravitational field itself. The usual meaning to spatital-temporal separation can be obtained from the state of the gravitational field on the boundary of the spacetime region considered.

 

[Giulio Prisco]

Can we say that the path integral over all spin foams that connect an input spin network I to an output spin network O is the probability amplitude PA(I,O) for I to be followed by O in a time sequence that emerges from the theory?
Can we say that the O with the highest P (PA squared in the usual sense) is the probable successor of I in a time sequence that emerges from the theory?
Can we say that this defines a time sequence in the classical limit?
If so, what is a good reference? I have been looking but everyone seems to keep as ambiguous as possible.

 

[Giulio Prisco]

There the idea is to study the boundary amplitude, namely a path integral over a finite space-time region, seen as a function of the boundary value of the field, peaked on a semi-classical state which, of course, includes the gravitational field itself. The usual meaning to spatital-temporal separation can be obtained from the state of the gravitational field on the boundary of the spacetime region considered.

Is there a good reference on this?