It might at first sight seem that there should be four degrees of freedom, as α {\displaystyle \alpha } and β {\displaystyle \beta } are complex numbers with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint |α|2 + |β|2 = 1, which can be treated as the equation for a 3-sphere embedded in 4-dimensional space with a radius of 1 (unit sphere). This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom.