# HQET Lagrangian identity

by Einj
Tags: hqet, identity, lagrangian
 P: 328 Hi everyone. I'm studying Heavy Quark Effective Theory and I have some problems in proving an equality. I'm am basically following Wise's book "Heavy Quark Physics" where, in section 4.1, he claims the following identity: $$\bar Q_v\sigma^{\mu\nu}v_\mu Q_v=0$$ Does any of you have an idea why this is true?? I think that an important identity to use in order to prove that should be $Q_v=P_+Q_v$, where $P_\pm=(1\pm \displaystyle{\not} v)/2$ are projection operators. Thanks a lot
 PF Gold P: 472 I thought it was because : (bear with me i dont remember the slash command for the forums right now) the equation of motion: $$v^{\mu}\gamma_{\mu} Q_v = Q_v$$ $$\bar{Q}_v v^{\mu}\gamma_{\mu} = \bar{Q}$$ so $$v_{\mu} \bar{Q} \left( \gamma^{\mu} \gamma^{\nu} - \gamma^{\nu} \gamma^{\mu}\right) Q$$ becomes $$\bar{Q} \left( \gamma^{\nu} - \gamma^{\nu} \right) Q$$