- #1

latentcorpse

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I'm trying to prove equation (5.15) in these notes:

http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

Just above eqn (5.15) we are told that the proof should be exactly the same as the proof of (5.5) which is done on p107.

I completely understand the proof on p107 for the commutation relations.

When trying to prove the anticommutation relations, the only difference is going to be a minus sign on the second term.

In other words, the proof is the same as on p107 except we have

[tex] \{ \psi( \vec{x}), \psi^\dagger \vec{y} \} = \displaystyle\sum_{s} \in \frac{d^3p}{(2 \pi)^3} \frac{1}{2E_{\vec{p}}} \left( u^s( \vec{p} \bar{u}^s(\vec{p}) \gamma^0 e^{i \vec{p} \cdot ( \vec{x}-\vec{y})} + v^s(\vec{p}) \bar{v}^s(\vec{p}) \gamma^0 e^{-i \vec{p} \cdot (\vec{x} - \vec{y})} \right) [/tex]

This means that if we follow through the next few steps on p107 we arrive at

[tex] \int \frac{d^3p}{(2 \pi)^3} \frac{1}{E_{\vec{p}}} ( p_i \gamma^i + m ) \gamma^0 e^{i \vec{p} \cdot ( \vec{x} - \vec{y} )}[/tex]

and as far as I can tell there is no way to make that into a delta function!

ANY HELP IS GREATLY APPRECIATED!