  We elaborate on Abelian complex scalar models, which are dictated by natural
actions (all couplings are of order one), at fixed and large global $U(1)$
charge in an arbitrary number of dimensions. The ground state $|
\upsilon\rangle$ is coherently constructed by the zero modes and the appearance
of a centrifugal potential is quantum mechanically verified. Using the path
integral formulation we systematically analyze the quantum fluctuations around
$| \upsilon\rangle$ in order to derive an effective action for the Goldstone
mode, which becomes perturbatively meaningful when the charge is large. In this
regime we explicitly show that the whole construction is stable against quantum
corrections, in the sense that any higher derivative couplings to Goldstone's
tree-level action are suppressed by appropriate powers of the large charge.
