Register to reply 
Advanced : HQET Derivative manipulation 
Share this thread: 
#1
Feb1314, 05:41 AM

PF Gold
P: 466

This is a semiadvanced question for anyone with HQET experience.
When you expand out the Lagrangian, as well as the wave functions, you get things like the equation of motion that are expressed in terms of the covariant derivative and the heavy quark velocity : [tex] \def\lts#1{\kern+0.1em /\kern0.65em #1} i (v\cdot D) h_v = \left(\frac{1}{2 m_Q} \lts{D}^2_{\perp}  \frac{i}{4 m_Q^2} \lts{D}_{\perp} (v \cdot D) \lts{D}_{\perp} + ...\right)h_v [/tex] So when constructing currents you have some really long products of these D operators. Is there a standard strategy to simplification? Such as moving all (v.D)'s to the left or right. I can come up with the commutation relations so that I can write a simple mathematica script that can rearrange them however I see fit, also getting me the sigma.G term. I'm just wondering if anyone out there has done anything where they could say "oh yeah, the fastest way is to just reqwrite it all in terms of etc etc then do etc.) As it stands now depending on the order I expand to its quite a long expression. (Also any direction to books or articles may be useful, though in articles it always seem they avoid including any code or tricks, and the only real books are like HQP Manohar/Wise. 


#2
Mar614, 05:39 PM

P: 305

In my opinion there no easy way to simplify currents. The HQET is a fairly complicated theory, but I can be wrong. Have you ever tried Neubert review? I don't know if it contains what you are looking for but it's a fairly good reference. Sometimes it can be complementary to Wise's book. The full title is: Matthias Neubert  Heavyquark symmetry



Register to reply 
Related Discussions  
Advanced Physics or Intro Physics? (Please read before posting in Advanced Physics)  Advanced Physics Homework  1  
Extremely Advanced Materials from Manipulation of Spacetime  General Physics  18  
1/2system braket manipulation  Advanced Physics Homework  6  
Correct Algebraic Manipulation of Partial Derivative Operations  Calculus & Beyond Homework  4  
PDF and CDF manipulation  Set Theory, Logic, Probability, Statistics  12 