# Non-local interaction in HQET

by Einj
Tags: hqet, interaction, nonlocal
 P: 324 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?
 Quote by Einj $$\mathcal{L}=\bar h_v iD\cdot v h_v+\bar h_vi\gamma_\mu D^\mu_\perp\frac{1}{iD\cdot v+2m_Q}i\gamma_\nu D_\perp^\nu h_v.$$ 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 $\frac{1}{iD\cdot v+2m_Q}$, which implies an integration over all x. Or you can expand it in a power series and get derivatives of all orders.