I am having one question... If we know the form of the effective Lagrangian, let's say the form:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]L= g (\bar{\psi}_{e} \gamma^{\mu} P_{L} \psi_{\nu})(\bar{\psi}_{p} \gamma_{\mu} P_{L} \psi_{n}) [/itex]

How can someone calculate the spin averaged invariant matrix [itex]\large M[/itex]?

I mean I can do the whole calculation if it's to have the [itex]u,v[/itex] in place of [itex]\psi[/itex]. I am having also a problem of seeing when this is done in QED scatterings too, since we know that [itex]M= j^{\mu}j_{\mu}[/itex] with [itex]j^{\mu}= \bar{\psi} \gamma^{\mu} \psi [/itex]...

but I don't know if I have the whole Dirac spinor [itex]\psi[/itex] what someone is supposed to do?

In most cases for the weak interaction, I'm seeing [itex]M[/itex] given by [itex]u,v[/itex] (like in Halzen & Martin)...

Thanks

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# Calculating the Invariant Matrix

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