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Gauge theories of gravity

  1. May 13, 2008 #1
    I am an Italian physicist working in the field of condensed matter and non-relativistic quantum mechanics. Unfortunately my background in general relativity is very poor. In the last few monthes, as a hobby I am trying to learn a little bit of general relativity.

    Besides reading textbooks on GR, searching on the web and on scientific journals, I found some interesting approaches of general relativity not based on the equivalence principle but on the gauge principle, namely the cornerstone of quantum field theory and the standard model.

    According to these approaches spacetime remains flat and gravitational forces arise as a consequence of (Lagrangian) invariance under arbitrary local spacetime translations.

    Maybe I missed more interesting and important papers on the subject . But I noticed the approach from the Cambridge group: arXiv:gr-qc/0405033v1
    (Authors: Lasenby, Doran and Gull) and also tha approach by a Chinese physicist Ning Wu
    (see e.g arXiv:hep-th/0112062 v2).

    The development of gravitation as a gauge theory, as I understand, is quite older than these papers, but older approaches seems to maintain curved spacetime. Also the Nobel laureate Frank Wilczek worked on such gauge approaches (he published a paper on phys. rev. lett.: IASSNS-HEP-97/142).

    The point is that these apporaches have been largely ignored by the scientific community.
    Thus I would like to hear from some expert if they are wrong, if they have some weakness,
    if these (and possibly others) gauge approaches in flat spacetime can be considered meaningful or not.
  2. jcsd
  3. May 13, 2008 #2
    An interesting book for you might be "Classical Fields" - Moshe Carmeli, World Scientific 1984. Chapter 10 deals with the gauge theory of gravitation.
    Last edited: May 13, 2008
  4. May 13, 2008 #3
    Whether these authors have been ignored is unknown to me... but I don't think the connection formulation of GR has "been largely ignored". However, they are less useful in classical GR and people have heavily investigated quantizing GR. Whether you use the metric or the connection as your fundamental variables, there seems to be no way of getting a renormalizable theory - which is why fewer people are working on it nowadays.
  5. May 14, 2008 #4
    Thank you both for your informations and suggestions.
    As a physicist not-expert in the field, even if gauge theories of gravity in flat spacetime are still non-renormalizable, I believe that they hold a better promise towards reconciliation with the standard machinery of QFT.
  6. May 14, 2008 #5
    Given that the standard machinery of QFT is renormalization, I don't agree with that statement.
  7. May 14, 2008 #6
    Of course predictivity of QFT is based on renormalization, but three of the four known interactions are introduced by the gauge principle. Hence, I think that the possiiblity of introducing the fourth (gravitation) by the same (or an analogous) principle is interesting and seems promising towards unification, even if the road may still be very long.
  8. May 14, 2008 #7


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    essential reading is 'On the Gauge Aspects of Gravity' by Gronwald and Hehl. Published in conference proceedings and on the arXiv gr-qc/9602013.

    Also, and in my view the coolest gauge theory is Teleparallel gravity which gauges the translation group and gives the same predictions as GR. An introductory paper is gr-qc/0312008, authors R. Aldrovandi, J. G. Pereira, and K. H. Vu.

    I have tried to understand Ning Wu's work but it eludes me. I'm still reading the Cambridge groups 'Geometric Algebra' approach.

    Last edited: May 14, 2008
  9. May 15, 2008 #8

    I found the two papes that you suggested very useful, moreover Aldrovandi and Pereira have published a paper on gauge gravity also on Phys. Rev. lett. I can be more confident on their papers then those of Ning Wu. Moreover they use a more traditional approach simpler to understand (for me) that the geometric algebra of the Cambridge grup.
    I am studying the papers that you suggested.
  10. May 15, 2008 #9


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    Aldrovandi and Pereira have a paper in the arXiv ( also in conference proceedings) arXiv:0801.4148, which I will read later.

    I'm not expert enough to say if these theories are flawed. I think Teleparallel is probably right, but it seems as difficult to quantize as GR.

    Some time I hope to put in the effort to understand geometric algebra. Quantizing space-time directly seems a good way to go.

    I also find it strange that so few schools are studying these non-GR theories.

  11. May 15, 2008 #10


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    Given that the standard theory applies GR to cosmological constraints and has to invoke Inflation, Dark matter and Dark Energy to fit, none of which have been discovered in laboratory physics, I find it more than strange!

  12. May 15, 2008 #11
  13. May 16, 2008 #12


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    Most modern classes in GR (particulalry if taught by a high energy physicist) will spend some time dealing with gravity formulated as a gauge theory. Weinberg's GR text is an example (although he uses idiosynchratic notation that masks the geometric content)

    Its a prerequisite if you want to study more advanced topics like quantum gravity or supergravity, but it doesn't really buy you anything if you are just interested in the classical vanilla theory (other than giving a nice unified picture).
  14. May 18, 2008 #13
    I think if you use a flat spacetime (euclidian) with rubbery rulers i.e. C and planck length and time. The effects on C and Planck lenght and time should increase on the inverse square as you go to energies relative to the event horizon........... I think you can predict the evolution in a stellar collapse and show through QCD a BH cooling process the inverse of E=MC2 resulting in GRB.. Then as the event horizon coallesese a Blackhole Rain would result through QCD and the fact that at the quark level quark and anti quarks do not anniliate. It forces you to a QGP evolutionary process demonstrating stellar mass BH. I think the cooling process extends to supermassice BH which would require T<. I.e. we will have to rethink BH entrophy.
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