# Non-local interaction in HQET

1. May 25, 2014

### Einj

Hi everyone. I have been studying the Heavy Quark Effective Theory and at a certain point we have a Lagrangian like:
$$\mathcal{L}=\bar h_v iD\cdot v h_v+\bar h_vi\gamma_\mu D^\mu_\perp\frac{1}{iD\cdot v+2m_Q}i\gamma_\nu D_\perp^\nu h_v.$$
$h_v$ is the field representing the heavy quark, $v$ is the velocity of the heavy quark and $D_\mu$ 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. May 26, 2014

### Hepth

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.

3. May 26, 2014

### Bill_K

It's because of the operator $\frac{1}{iD\cdot v+2m_Q}$, which implies an integration over all x. Or you can expand it in a power series and get derivatives of all orders.

4. May 26, 2014

### Einj

Great, thanks!