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Why is the probability for each momentum in a loop (e.g. vacuum polarization) equal?

Why has a infinite momentum the same probability to occur than a virtual particle with low moment. I know - these particels are virtual and in some sense not physically.

But at the end, we want to describe our universe - so in some sense it should be physically. The point with the same probability is not intuitiv for me.

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It has been explained several times on this site - see e.g. Virtual Particles real? Virtual particles create a universe? - that you cannot think of virtual particles as real particles, let alone think of the momentum integration as some probability of having that momentum. The integration over the loop momenta follows directly from the perturbative expansion; it is a mathematical device only.

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