RedX
Oct23-09, 12:04 AM
A Dirac field can be written as two Weyl fields stacked on top of each other: \Psi= \left( \begin{array}{cc} \psi \\ \zeta^{\dagger} \end{array}\right) , where the particle field is \psi and the antiparticle field is \zeta.
So a term like P_L\Psi=.5(1-\gamma^5)\Psi=\left( \begin{array}{cc} \psi \\ 0 \end{array}\right) should only involve the particle and not the antiparticle?
However, writing \Psi=\Sigma_s \int d^3p \mbox{ } [b_s(p)u_s(p)e^{ipx}+d_{s}^{\dagger}(p)v_s(p)e^{-ipx}] , some of the antiparticle gets involved when projecting it with P_L since P_L v_s(p) is not necessarily zero?
Is the interpretation that \psi is a particle, and \zeta is an antiparticle, wrong then?
So a term like P_L\Psi=.5(1-\gamma^5)\Psi=\left( \begin{array}{cc} \psi \\ 0 \end{array}\right) should only involve the particle and not the antiparticle?
However, writing \Psi=\Sigma_s \int d^3p \mbox{ } [b_s(p)u_s(p)e^{ipx}+d_{s}^{\dagger}(p)v_s(p)e^{-ipx}] , some of the antiparticle gets involved when projecting it with P_L since P_L v_s(p) is not necessarily zero?
Is the interpretation that \psi is a particle, and \zeta is an antiparticle, wrong then?