## Wick rotation and Minkowski/Euclidean space

Hello, I was wondering why in integrals such as
$$\int d^4k F(k^2)$$
where $$k^2 = (k^0)^2 - |\vec{k}|^2$$ ranges from -∞ to ∞, once the Wick-rotation is performed, we have $$-k^2_E = -(k^0_E)^2 - |\vec{k}_E|^2$$ which lies in the (-∞,0) interval ... So, the contribution which lies in the part where $$k^2 >0$$ it seems that fades away. This function would have even poles. It is still a bit counter-intuitive for me that this part just fades away.

I guess we could shift the space-variables as $$\vec{k} \rightarrow \vec{k+k_0}$$ so this always lays in the euclidean space so to say. Anyway I am not sure, if this shift is always allowed.

Asides, things get more annoying for me if we have other four-vectors in the function, appart that the loop variable, which are Minkowskian, i.e. $$F((k+q)^2,(k-p)^2)$$ where $$q^2 = m^2, \ p^2 = M^2$$ (both are positive quantities) ...

I find this kind of examples in triangle loops diagrams where the function F(k,q,..) is the form factor, and I this form factor is supposed to be the in the Spacelike or Euclidean region ...

Thanks in advance!
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 Tags euclidean space, euclideanization, form factor, loop integrals

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