Wick rotation and Minkowski/Euclidean spaceby Pablo88 Tags: euclidean space, euclideanization, form factor, loop integrals 

#1
Feb1013, 10:14 AM

P: 1

Hello, I was wondering why in integrals such as
[tex] \int d^4k F(k^2) [/tex] where [tex] k^2 = (k^0)^2  \vec{k}^2 [/tex] ranges from ∞ to ∞, once the Wickrotation is performed, we have [tex] k^2_E = (k^0_E)^2  \vec{k}_E^2 [/tex] which lies in the (∞,0) interval ... So, the contribution which lies in the part where [tex] k^2 >0[/tex] it seems that fades away. This function would have even poles. It is still a bit counterintuitive for me that this part just fades away. I guess we could shift the spacevariables as [tex] \vec{k} \rightarrow \vec{k+k_0} [/tex] 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 fourvectors in the function, appart that the loop variable, which are Minkowskian, i.e. [tex] F((k+q)^2,(kp)^2) [/tex] where [tex] q^2 = m^2, \ p^2 = M^2 [/tex] (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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