Are there any linear quantum gravity theories?

[Nickyv2423]

Are there any linear quantum gravity theories out there with respect to the wave function?

 

[dextercioby]

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.

 

[Demystifier]

Are there any linear quantum gravity theories out there with respect to the wave function?

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.

 

[haushofer]

Maybe you're confusing fields with wave functions ?

 

[Demystifier]

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.

 

[haushofer]

I meant the OP. If so, the question seems to make more sense to me.

 

[Nickyv2423]

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.

What about asymptotic safety in quantum gravity?

 

[Demystifier]

What about asymptotic safety in quantum gravity?

It's also linear.

 

[Nickyv2423]

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.

 

[Demystifier]

Casual fermion systems is non linear and so is casual dynamical triangulation.

Can you support it by a reference?

 

[Nickyv2423]

Can you support it by a reference?

I just emailed researchers in the field and they told me.

 

[Demystifier]

I just emailed researchers in the field and they told me.

Can you copy/paste the exact question you asked and their exact answer?

 

[Nickyv2423]

Can you copy/paste the exact question you asked and their exact answer?

Me -
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 -
Dear Nick,

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
https://arxiv.org/abs/1502.03587
or the first chapter of the book
https://arxiv.org/abs/1605.04742
The connection to quantum geometry (which should also be the framework for describing quantum gravity) is worked out in
https://arxiv.org/abs/1107.2026

Just let me know if you have any further questions.

Felix

 

[Nickyv2423]

Can you copy/paste the exact question you asked and their exact answer?

I don't have the reply from the CDT researcher I deleted it

 

[Demystifier]

For more information you could have a look at the survey paper
https://arxiv.org/abs/1502.03587

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.

 

[Physics4Funn]

Thank you for looking at this CFS paper.
It's not the best place to start reading Finster's work as he has papers going back about 15 years.

I know Finster's approach is different, but considering how many smart people have looked at QG and UFT and made such limited progress, I consider even the nut cases worthy of a look.

So far I have found many new and useful ideas in Finster's CFS papers.
The basic concepts are appealing.
I have not found any errors so I am still studying it.

I posted a preprint using Finster's model looking for connections to dark matter.

In another thread about the Dirac sea, the only slightly more specific reply was that Finster's Dirac sea extension has many objections.
If you have specific objections, I will eagerly read them.
I'll post in the other thread next.

Thank you for any help as I have been looking for anyone has any comments about it.