Register to reply

Non-local interaction in HQET

by Einj
Tags: hqet, interaction, nonlocal
Share this thread:
Einj
#1
May25-14, 06:50 PM
P: 321
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?
Phys.Org News Partner Physics news on Phys.org
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Bubbling down: Discovery suggests surprising uses for common bubbles
New non-metallic metamaterial enables team to 'compress' and contain light
Hepth
#2
May26-14, 04:57 AM
PF Gold
Hepth's Avatar
P: 469
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: 321
Non-local interaction in HQET

Great, thanks!


Register to reply

Related Discussions
HQET Lagrangian identity High Energy, Nuclear, Particle Physics 7
Advanced : HQET Derivative manipulation High Energy, Nuclear, Particle Physics 1
P(x) has two local maxima and one local minimum. Answer the following Calculus & Beyond Homework 2
Weih's data: what ad hoc explanations do local and non-local models give? Quantum Physics 60
A proof that all signal local theories have local interpretations. Quantum Physics 3