  The multiplicative and the functional renormalization group methods are
applied for the four dimensional scalar theory in Minkowski space-time. It is
argued that the appropriate choice of the subtraction point is more important
in Minkowski than in Euclidean space-time. The parameters of the cutoff theory,
defined by a subtraction point in the quasi-particle domain, are complex due to
the mass-shell contributions and the renormalization group flow becomes much
more involved than its Euclidean counterpart.
