That’s a good question. I need to check it out. I can’t tell you right off the bat because I’m rusty with CFT and my research is in probability theory, although we are observing connections with CFT. Now, suppose I do have crossing symmetry, then the answer is yes? And if I don’t, the answer is no?

That's for the case of fermionic $t$'s. But if they were bosonic? Can this calculation even be made? Wouldn't I obtain just $\det(A)$ in that case?

Funny enough, I ran across that paper yesterday. So basically the second derivation in my calculations wouldn't make sense for bosonic $t$. Does that mean that the first calculation (where I obtain the answer $\det(A)$) is the correct one? I know it sounds strange that I need bosonic $t$, but for my research I need to compute the characteristic function of a gaussian vector with fermionic variables, and compare it to the bosonic case. That's why I try and use boson $t$ in both cases. But maybe everything is ill-defined from the beginning.

Crook's theorem is one of the most beautiful things I saw in thermodynamics. It's quite amazing it took until mid 90' for people to discover it.

Yes, instead of assuming a maximum speed it would probably be better to say that we have a pseudo-Riemannian metric which is locally Minkowski. So in my case, no SR would mean to have a degenerate metric split into time and space, which is locally Galilean. But that would be the case of the Newton-Cartan Theory as mentioned by G. Smith, right? Wouldn't all the machinery work anyway in this case? What I don't know is if it would be the same as GR with $c\to\infty$, or if it would predict the same results as Newtonian mechanics.

@CRDrost Making $c\to\infty$ (ie, no SR) implies, for example, that the Schwarzschild radius goes to $0$, so there would be no BHs in the theory. And in the same way there would be no time dilation. But I'm not sure whether $c\to\infty$ abolishes any sort of curvature, and if so, how gravity comes up.

Interesting! Do you know if the predictions of the theory match exactly those of Newton? And would it also match the case of GR with $c\to\infty$?

So it's only when considering wave-packets that we can really speak about non interaction at large distances?