Are there any linear quantum gravity theories out there with respect to the wave function?
You can quantize the (Pauli-Fierz) free spin-2 field (which is the 1st order perturbation of the space-time metric) canonically or better yet with path integrals as normal linear QFT (just like electromagnetism in Minkowski spacetime). There's a (probably the best) chapter of Zee's book on QFT on this. The Pauli-Fierz action is deducted by Feynman in his GR book from symmetry considerations.
All mainstream quantum gravity theories (string theory, Wheeler-DeWitt, loop quantum gravity, perturbative quantization of spin-2 field in a classical background, etc.) are linear with respect to the wave function. Linearity (or superposition principle) is one of the basics axioms of quantum theory.
Maybe you're confusing fields with wave functions ?
Who are you referring to? The OP stated that he is talking about linearity with respect to wave functions. I assumed that by "wave functions" he means quantum states and not the gravitational fields. Dextercioby assumed the opposite.
I meant the OP. If so, the question seems to make more sense to me.
What about asymptotic safety in quantum gravity?
It's also linear.
How do you know? Not all quantum gravity theories are linear. Casual fermion systems is non linear and so is casual dynamical triangulation.
Can you support it by a reference?
I just emailed researchers in the field and they told me.
Can you copy/paste the exact question you asked and their exact answer?
Hello, I know this is random but I just have a simple question concerning Casual Fermion System (CFS) as a theory of quantum gravity...
Is CFS a local or non local theory of Quantum Field Theory? If it is local, then it cannot be correct. Also, is CFS linear with respect to the wave function?
Felix Finster -
Thanks for your question! I am sorry for not writing back earlier.
The causal action principle (which gives rise to the physical equations in a causal fermion system) is non-linear and non-local. But of course, the resulting Euler-Lagrange equations are linear in certain limiting cases, in particular giving rise to a linear dynamics on Fock spaces.
For more information you could have a look at the survey paper
or the first chapter of the book
The connection to quantum geometry (which should also be the framework for describing quantum gravity) is worked out in
Just let me know if you have any further questions.
Best regards, Felix
I don't have the reply from the CDT researcher I deleted it
You are right, this is really a non-linear theory with respect to the quantum state (which you call wave function). The theory has something to do with the so-called wave-function collapse. However, this is a very exotic theory, very very far away from the mainstream.
Asymptotic safety, however, is quite mainstream. As I said, all mainstream theories of quantum gravity are linear.
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