  A phase-space representation of nuclear interactions, which depends on the
distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is
presented. A method is developed that permits to extract the interaction
$V(\vec{r},\vec{p})$ from antisymmetrized matrix elements given in a spherical
basis with angular momentum quantum numbers, either in momentum or coordinate
space representation. This representation visualizes in an intuitive way the
non-local behavior introduced by cutoffs in momentum space or renormalization
procedures that are used to adapt the interaction to low momentum many-body
Hilbert spaces, as done in the unitary correlation operator method or with the
similarity renormalization group. It allows to develop intuition about the
various interactions and illustrates how the softened interactions reduce the
short-range repulsion in favor of non-locality or momentum dependence while
keeping the scattering phase shifts invariant. It also reveals that these
effective interactions can have undesired complicated momentum dependencies at
momenta around and above the Fermi momentum. Properties, similarities and
differences of the phase-space representations of the Argonne and the N3LO
chiral potential, and their UCOM and SRG derivatives are discussed.
