nor does it commute with the ladder operators, so one must pay close attention to how the operators are used. There is, however, a simple braiding relation, D ^ ^ ( α α ) S ^ ^ ( z ) = S ^ ^ ( z ) S ^ ^ † † ( z ) D ^ ^ ( α α ) S ^ ^ ( z ) = S ^ ^ ( z ) D ^ ^ ( γ γ ) , where γ γ = α α cosh ⁡ ⁡ r + α α ∗ ∗ e i θ θ sinh ⁡ ⁡ r