In Gross-Pitaevskii mean field theory, one replaces the field operators with c-number functions:
.  To find the mean-field
ground states, one then minimises the resulting energy with respect to these c-number functions.
For a spatially uniform system spin-one system, there are two possible mean-field ground states.  
When , the ground state is
while for  the ground state is 
The former expression is referred to as the polar state while the latter is the 
ferromagnetic state.
Both states are unique up to overall spin rotations.  Importantly, 
cannot be rotated into .
The Majorana stellar representation 
 provides a particularly insightful description of the mean-field phases of spinor 
condensates with larger spin.