contains a singularity that cannot be regulated using dimensional regularization. For bubble diagrams and those $N$-point functions that are known to be real-valued, the choice of regulator is in principle free, but the most straightforward prescription is to interpret the diverging integrations in a principal value sense. For correlators that might develop physical imaginary parts upon a specific $i\epsilon$ prescription, the procedure is, however, more tricky and one must be careful not to discard any physically meaningful contributions.

Discussion and outlook \[sec:conc\]
===================================

The cutting rules we stated and proved in the previous three sections apply as such only under the assumptions listed in sec. \[sec:state\]. It is, however, straightforward to see that the first three of the conditions can be easily relaxed:

-   The appearance of external or internal momenta in the numerator of the Feynman graph does not prohibit the application of the cutting rules. The only potential problem might originate from 0-components of internal momenta, but even these will simply be replaced by the corresponding $iE_i$ factors according to the Residue Theorem.

-   If a scalar propagator is raised to a higher power, care must be taken when evaluating the Feynman integral. The most straightforward way to 