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I doubted whether to post this in the homework section, but decided not to because a) it's only a very small part and b) I think my question is important in general.

Looking at page 107 of Zee's Introduction to QFT I am trying to get from (16) to (17). For this I need to evaluate several "inner" products like

[tex]\sum_{\alpha} (u^\dagger)^\alpha(p, s) u_\alpha(p, s')[/tex]

and

[tex]\sum_{\alpha} (v^\dagger)^\alpha(p, s) u_\alpha(-p, s')[/tex]

where - using standard notation, I think, u and v are the amplitudes of plane wave solutions [itex]u(p, s) e^{-i \vec p \cdot \vec x}[/itex], [itex]v(p, s) e^{i \vec p \cdot \vec x}[/itex] of the Dirac equation.Question:How do I do that?

It's also somewhat related to page 105 of Zee, where he calculates

[tex]\sum_s u_\alpha(p, s) \overline u_\beta(p, s) = \frac12 (\gamma^0 + 1)_{\alpha\beta}[/tex]

(and similarly for u -> v) in the rest frame and then without any explanation jumps to the general (8) and (9),

[tex]\sum_s w_\alpha(p, s) \overline w_\beta(p, s) = \left( \frac{\gamma^\mu p_\mu \pm m}{2m} \right)_{\alpha\beta}[/tex]

(with the plus sign for w = u and minus for w = v).

Apart from the fact I don't really see how he does that, I also don't think it will work for my question above, as [itex]u^\dagger u[/itex] is not an invariant, so we cannot first calculate it in the rest frame [plus I am not summing over s].

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# Summing spinor products

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