"Local observables" at some point in the manifold don't exist, precisely because you can do a diffeomorphism and move everything to somewhere else in the manifold. But the observable "curvature at the point identified by GPS readings (a,b,c,d)" is physically well defined. One could hope to have...
Why do you claim that the manifold "exists", and in what sense? That is not the way I usually hear people talking about LQG. They usually speak as if the amplitudes for the various graphs and their vertex/edge observables are the full content of the state; i.e. "all that is".
I also don't...
I don't see that he's saying that. AdS/CFT never made any claim that our universe should be AdS. Their claim is that the duality defines a quantum gravity theory, which happens to live in AdS. Hopefully, gravity in our world works more-or-less similarly to how it works in AdS, at least as far as...
It is actually quite similar to the standard Transverse Traceless (TT) gauge. It might even be identical; I'm not sure about that. Kind of ironic that Weinberg calls his gauge "too ugly to deserve a name"! Was TT gauge in use for gravitational waves, back in 1965?
Anyhow, none of the classical...
Hey, good to see you're still around! I've been away from PF for a while, but when I come back I get my first response from an old friend!
DeWitt's work is certainly very central and powerful, but I'm specifically interested in the "Coulomb-gauge" approach developed by Weinberg in that paper. I...
In this 1965 paper by Weinberg, https://journals.aps.org/pr/abstract/10.1103/PhysRev.138.B988, he describes a quantum field theory of the graviton in a Coulomb-like fixed gauge, where the free graviton has only space-space components and is traceless. This of course makes the field dynamics...
In the article, you mention the hope that a "suitable summation scheme" will be found for Causal Perturbation Theory, thus proving the rigorous existence of ##S(g)##. To me this hope seems unsupported and wildly optimistic. Remember that this is a power series in ##g##, so we need is a summation...
I think my post does belong on this thread. The original post was a paper saying that we should consider "the real QFT" to mean QFT-with-cutoff, rather than a supposed continuum theory. That is the point I am trying to argue here: that it is likely that QFT does not have a rigorous UV limit at...
Because some comments have been moved, I will reproduce the reevant part of the conversation before responding:
Okay, I admit that this axiom-based approach is more successful than I gave it credit for. It's not just "here is a well-defined algorithm that that reproduces what physicists...
What? I am talking about processes like ##e \rightarrow e+ \gamma.## When ##g=1## this cannot happen because of conservation laws, but otherwise it should occur already at first order in perturbation theory.
But this raises another issue: Per the axioms, ##S(g)## should not take us out of single-particle subspaces. But without 4-momentum conservation, won't a single fermion have an amplitude to spontaneously emit photons?
##g## is the test function that switches on the interaction, correct? So anything first-order in ##g## is also first-order in ##e##.
Oh, I think I see. You are saying that since ##g(x)## is not translation-invariant, energy and momentum are not conserved by ##S(g)##, and so first-order...