  Functional renormalization yields a simple unified description of bosons at
zero temperature, in arbitrary space dimension $d$ and for $M$ complex fields.
We concentrate on nonrelativistic bosons and an action with a linear time
derivative. The ordered phase can be associated with a nonzero density of
(quasi) particles $n$. The behavior of observables and correlation functions in
the ordered phase depends crucially on the momentum $k_{ph}$, which is
characteristic for a given experiment. For the dilute regime $k_{ph}\gtrsim
n^{1/d}$ the quantum phase transition is simple, with the same ``mean field''
critical exponents for all $d$ and $M$. On the other hand, the dense regime
$k_{ph}\ll n^{1/d}$ reveals a rather rich spectrum of features, depending on
$d$ and $M$. In this regime one observes for $d\leq 3$ a crossover to a
relativistic action with second time derivatives. This admits order for $d>1$,
whereas $d=1$ shows a behavior similar to the low temperature phase of the
classical two-dimensional $O(2M)$-models.
