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I Are there any linear quantum gravity theories?

  1. Jan 4, 2017 #1
    Are there any linear quantum gravity theories out there with respect to the wave function?
     
  2. jcsd
  3. Jan 4, 2017 #2

    dextercioby

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    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.
     
  4. Jan 5, 2017 #3

    Demystifier

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    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.
     
  5. Jan 5, 2017 #4

    haushofer

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    Maybe you're confusing fields with wave functions ?
     
  6. Jan 5, 2017 #5

    Demystifier

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    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.
     
  7. Jan 6, 2017 #6

    haushofer

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    I meant the OP. If so, the question seems to make more sense to me.
     
  8. Jan 18, 2017 #7
    What about asymptotic safety in quantum gravity?
     
  9. Jan 19, 2017 #8

    Demystifier

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    It's also linear.
     
  10. Jan 19, 2017 #9
    How do you know? Not all quantum gravity theories are linear. Casual fermion systems is non linear and so is casual dynamical triangulation.
     
  11. Jan 19, 2017 #10

    Demystifier

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    Can you support it by a reference?
     
  12. Jan 19, 2017 #11
    I just emailed researchers in the field and they told me.
     
  13. Jan 19, 2017 #12

    Demystifier

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    Can you copy/paste the exact question you asked and their exact answer?
     
  14. Jan 19, 2017 #13
    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.

    Best regards, Felix
     
  15. Jan 19, 2017 #14
    I don't have the reply from the CDT researcher I deleted it
     
  16. Jan 19, 2017 #15

    Demystifier

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    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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