Currently, to_euler_phases returns
zₐ ≔ exp(i*α)
zᵦ ≔ exp(i*β)
zᵧ ≔ exp(i*γ)
Presumably, the main consumer of this is SphericalFunctions's Wigner D and sYlm stuff, which exponentiate zₐ and zᵧ by $-m'$ and $-m$, respectively.
This is a bit more complicated than necessary; the more natural things to return are
z₊ ≔ exp(i*(α+γ)/2)
z₀ ≔ exp(i*β)
z₋ ≔ exp(i*(α-γ)/2)
Here, we would exponentiate z₊ and z₋ by $-m'-m$ and $-m'+m$, respectively. This would simplify half-integer cases a bit, but more importantly, I suspect that it might give slightly better results in some cases — possibly near β=π or 0.
I feel like that function should be called to_spinor_phases or something.
Currently,
to_euler_phasesreturnsPresumably, the main consumer of this is$-m'$ and $-m$ , respectively.
SphericalFunctions's Wigner D and sYlm stuff, which exponentiatezₐandzᵧbyThis is a bit more complicated than necessary; the more natural things to return are
Here, we would exponentiate$-m'-m$ and $-m'+m$ , respectively. This would simplify half-integer cases a bit, but more importantly, I suspect that it might give slightly better results in some cases — possibly near β=π or 0.
z₊andz₋byI feel like that function should be called
to_spinor_phasesor something.