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Non-local interaction in HQET

  1. May 25, 2014 #1
    Hi everyone. I have been studying the Heavy Quark Effective Theory and at a certain point we have a Lagrangian like:
    \mathcal{L}=\bar h_v iD\cdot v h_v+\bar h_vi\gamma_\mu D^\mu_\perp\frac{1}{iD\cdot v+2m_Q}i\gamma_\nu D_\perp^\nu h_v.
    [itex]h_v[/itex] is the field representing the heavy quark, [itex] v[/itex] is the velocity of the heavy quark and [itex]D_\mu[/itex] is the usual covariant derivative.

    I read that this Lagrangian is non-local but I can't understand why. Do you have any idea?
  2. jcsd
  3. May 26, 2014 #2


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    Is it because you're choosing what the momentum "v" is? Therefor things are no longer technically lorentz invariant, as the theory only holds in the limit that v is "stationary". Basically you're choosing a specific POV to choose the problem.
  4. May 26, 2014 #3


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    It's because of the operator [itex]\frac{1}{iD\cdot v+2m_Q}[/itex], which implies an integration over all x. Or you can expand it in a power series and get derivatives of all orders.
  5. May 26, 2014 #4
    Great, thanks!
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