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I interested in different approaches to quantum gravity.

Insofar I understand string-theory correctly, it constitutes a $S$-matrix theory. E.g., David Tong writes

The object that we can compute in string theory is the S-matrix. This is obtained by taking the points in the correlation function to infinity: $x_i \to \infty$

Now my question:

Is loop quantum gravity essentially also an S-matrix theory, i.e., the thing it allows you to calculate is the asymptotic S-matrix. Or is it possible to make predictions, beyond the S-matrix. If it is more than just an S-matrix theory, what are the (diff invariant) observables of loop quantum gravity?

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    $\begingroup$ Suggestion for the title (v2): Does loop quantum gravity have an $S$-matrix? $\endgroup$ Commented Sep 23, 2024 at 10:04
  • $\begingroup$ @Qmechanic My question was more about predictions beyond the $S$-matrix. Maybe something like black hole to white hole transitions. But if I understand you correctly, it is not even clear if there is an $S$-matrix in LQG at all. Is this correct? $\endgroup$ Commented Sep 23, 2024 at 12:38

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