1 so 1 5 acts as a projecbon operator

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Unformatted text preview: p = p ⋅ Σ u p where Σ ≡ ⎜ ⎟ 0 σ⎠ ⎝ () ( )() ˆ Recall that Σ is the spin matrix for a Dirac parBcle (see secBon 7.2), so p ⋅ Σ 2 ( ) represents the helicity, with eigenvalues of ±1. ( ) 1 So we have that 1 − γ 5 u ( p ) = 0 if u ( p) carries helicity +1 (right handed) 2 = u p ) if u( ) carries helicity  ­1 (le] handed) ( p Reminder: this is true in the massless limit only; for small masses it is approximate. ( ) 1 So 1 − γ 5 acts as a projecBon operator that picks out the helicity  ­1 component 2 4 If the parBcle is NOT massless it is only in the ultra ­relaBvisBc regime ( E > > c 2 ) that m γ u( p) = 5 ( p ⋅ Σ u( p) ) holds approximately, and it is only in this limit that...
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