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?
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.
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.