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Non-local interaction in HQET

by Einj
Tags: hqet, interaction, nonlocal
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Einj
#1
May25-14, 06:50 PM
P: 328
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?
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Hepth
#2
May26-14, 04:57 AM
PF Gold
Hepth's Avatar
P: 472
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.
Bill_K
#3
May26-14, 05:25 AM
Sci Advisor
Thanks
Bill_K's Avatar
P: 4,160
Quote Quote by Einj View Post
$$
\mathcal{L}=\bar h_v iD\cdot v h_v+\bar h_vi\gamma_\mu D^\mu_\perp\frac{1}{iD\cdot v+2m_Q}i\gamma_\nu D_\perp^\nu h_v.
$$

I read that this Lagrangian is non-local but I can't understand why. Do you have any idea?
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.

Einj
#4
May26-14, 09:15 AM
P: 328
Non-local interaction in HQET

Great, thanks!


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