# Can the rate of virtual pair production from vacuum be computed?

Consider for instance the QED Lagrangian. Is it possible to compute the rate of virtual electron-positron creation from the vacuum?

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If you want to consider this in terms of QED, then it is easy. Virtual pair production-annihilation is described by a vacuum bubble diagram where two propagators a contracted into a loop and there are no external legs. These kinds of diagrams are usually thrown away when we consider the partition function of the theory. And there is a good reason for that, as the matrix element of this diagram diverges at momentum $0$ running around the loop. So you might say that the rate of this process is infinite, whatever this means.