Expressing Feynman Green's function as a 4-momentum integral

In summary, the conversation discusses the use of (z',p) as a 4-vector and the confusion surrounding its interpretation. The speaker questions the validity of using a new variable in forming a 4-vector with momentum and the change in interpretation of z' as a result. The conversation also mentions the use of ##\theta(x^0 - y^0)## and its preservation of time orientation in the restricted Lorentz group. The rest of the conversation involves expressing this in momentum space.
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I am a bit confused on how we can just say that (z',p) form a 4-vector. In my head, four vectors are sacred objects that are Lorentz covariant, but now we introduced some new variable and say it forms a 4-vector with momentum. I understand that these are just integration variables but I still do not see how this is okay. The interpretation of z' now is different.

I am a bit confused on how we can just say that (z',p) form a 4-vector. In my head, four vectors are sacred objects that are Lorentz covariant, but now we introduced some new variable and say it forms a 4-vector with momentum. I understand that these are just integration variables but I still do not see how this is okay. The interpretation of z' now is different.
But where did it come from? ##\theta(x^0 - y^0)##, right? The restricted Lorentz group (identity-connected part) preserves time orientation, so it's ok to use ##\theta(x^0 - y^0)## in that circumstance. The rest just involves expressing it in momentum space.

vanhees71

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