possible $\mu$ in the external legs of the original graph).

Moving on to the terms with two or more $\theta$-function factors, the above reasoning goes through in each case, leaving us with the 2-, 3-, ..., and $N$-cut contributions to the original graph. In each case, the generated amplitudes are to be evaluated assuming the external momenta to be real: only afterwards are the cut momenta placed on-shell.

One final comment is in order. Each time some number of fermion lines are cut in a given Feynman graph, it follows from the construction presented above that these propagators must form a subset of some possible choice of integration momenta $S_r\in S$. This means that the cuts can never split the original 1PI graph into two (or more) disconnected pieces: for this to happen, we would need to cut propagators whose momenta are not linearly independent, which is not possible for any subset of $S_r$.

Regularization of the integrals \[sec:reg\]
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Before we can successfully apply the cutting procedure to an arbitrary Feynman diagram, there is one further issue that needs to be discussed. This is related to the regularization of unphysical divergences appearing in the calculations, of which there are 