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Weinberg-Witten Theorem and Quantum Gravity

  1. Nov 2, 2012 #1


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    Can someone who understands it explain the significance of the
    Weinberg-Witten Theorem to the possibility of quantum gravity?
    (Described here: http://en.wikipedia.org/wiki/Weinberg-Witten_theorem)

    From the Wikipedia article, the conclusion is
    I don't understand how that can be correct. Deser and Feynmann
    (independently?) showed that General Relativity can be understood (at
    least in asymptotically flat spacetimes) as the field theory of a spin-2
    massless particle whose source is the total stress-energy tensor. I know
    that this approach is not renormalizable, at least not in any obvious
    way, but it seems to conflict with the Weinberg-Witten Theorem. Is the
    WWT in some way a proof that the Deser/Feynmann theory is not

    One thing that is a little confusing about the Deser/Feynmann theory is
    exactly what the stress-energy tensor is. The assumption is that the
    spin-two particle couples to the total stress-energy, including the
    stress-energy of the particle itself. This is apparently very different
    from GR, in which the appropriate stress-energy tensor has no
    contribution due to gravity. I don't have a good grasp of how this is
  2. jcsd
  3. Nov 2, 2012 #2


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    "The Weinberg–Witten theorem states that a massless particle of spin strictly greater than one cannot possess an energy-momentum tensor Tμ which is both Lorentz covariant and gauge invariant. Of course, this no-go theorem does not preclude gravitational interactions. In the spin-two case, it implies that there cannot exist any gauge-invariant energy-momentum tensor for the graviton."

    More discussion here:

    "However, in [24, 25] it is pointed out that the obtained pseudotensor of the gravitational field is still Lorentz covariant, even though not generally covariant. Thus, at first sight, the Weinberg-Witten theorem appears to be applicable to this tensor. However, the crucial point seems to be again that these pseudotensors are constructed in the context of a classical, i.e. a non-quantum theory. ...

    "The process of constructing the energy-momentum pseudotensor for the gravitational field in a classical theory only breaks general covariance, not Lorentz covariance. Constructing a quantum field then requires additional terms under Lorentz transformations. To maintain Lorentz covariance of the theory, these additional terms would have to be eliminated by gauge transformations requiring general covariance. Like for the gluon, this gauge invariance of the current is not given for the graviton."
    Last edited: Nov 2, 2012
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