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Spin and torsion of the connection

  1. Aug 25, 2014 #1

    I read in an article that in GR it is possible to use a connection with torsion to model ponctual particle with spin. The connection can be decomposed in a curvatue part and a torsion part. In an other part, we know that the invariance under pointcarré group imply conservation of spin of particle. Can i conclude with a lot of prudence that a particle with spin is a exitation of the connection in GR ?

    I say this because boson are quantification of field that is, for yang mills theory, the value of the connection.

  2. jcsd
  3. Aug 25, 2014 #2


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    If there's spin, there no GR anymore. If there's a torsion, there's no GR anymore. So your first statement is inaccurate. What one needs to read is Hehl's work on Poincare gauge theory, which can be seen as a semi-classical extension of GR.
  4. Aug 26, 2014 #3


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    I would propose to start reading a few papers regarding Einstein-Cartan-Gravity, which is the most simple and natural extension of GR in the presence of spin.

    The interesting thing is that torsion couples to the spin density but is non-propagating; so there are no torsion-waves (gravitational waves are pure curvature-waves). In vacuum (vanishing energy-momentum / vanishing spin density) there is no torsion and the theory reduces to GR. Inside matter (non-vanishing energy-momentum / non-vanishing spin density) there can be torsion but its effects are highly suppressed.

    So in essence GR and Einstein-Cartan-Gravity are different mathematically, but indistinguishable experimentally!
  5. Aug 27, 2014 #4
    I am so sad, because i work with someone who prove that rotational waves in matérials have a fermionic behaviour (standard compression waves are bosonic). So, i was thinking that, may be, fermions appear when a quantification of the torsion of the connection is done. But if torsion is non propagative, it fail. Thanks for your answer, i will read the paper you speak about.

  6. Aug 27, 2014 #5


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    but within the material torsion could propagate b/c the spin current of the material does!

    but sorry, I can't say anything regarding effective quasi-particle theories with fermionic d.o.f. + Einstein-Cartan
  7. Aug 27, 2014 #6
    Are you sure about that statement? I thought Einstein-Cartan allows violation of conservation of angular momentum and of spin, conserving only the sum of the two. So it is certainly experimentally distinguishable from GR, which conserves angular momentum strictly.
  8. Aug 27, 2014 #7


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    I have to check the calculations but as far as I remember the effects are measurable in principle, not in practice. Either there is isolated spin (e.g. from elementary particles) and therefore GR / ECT effects are not measurable, or there are macroscopic GR / ECT effects due to angular momentum, but then the violations due to spin are suppressed. So as far as I can see there is no known experimental setup which can distinguish between GR and ECT.
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