  We discuss the quantum phases and their diffusion in a spinor-1 atomic
Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact
ground state distribution of the phase fluctuations corresponding to the total
atom number ($N$), the magnetization (${\cal M}$), and the alignment (or
hypercharge) ($Y$) of the system. The mean field ground state is shown to be
stable against these fluctuations, which dynamically recover the two continuous
symmetries associated with the conservation of $N$ and ${\cal M}$ as in current
experiments.
