I have often heard that R2 gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?
My naive understanding is that if the the Hamiltonian is hermitian then the S-matrix ⟨out∣S∣in⟩=limT→∞⟨out∣e−iH(2T)∣in⟩
must be unitary by definition. So why is this not the case for R2 gravity?
I see that Luboš Motl has a nice discussion related to such things here, but I am not sure which, if any, of the reasons he mentions relate to R2 gravity.
Are there other well known theories that have similar problems?
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