# Wigner-D in MMA

Can some nice MMA fellow explain to me why buit-in Wigner-D function is defined as

$D_{mm'}^{J} = e^{i(\phi m+ \gamma m')} d_{mm'}^{j}(\theta)$

against the convention, used by most people on Earth, ex.,

$D_{mm'}^{J} = e^{-i(\phi m+ \gamma m')} d_{mm'}^{j}(\theta)$

Just curious...

P.S.: I hope I just mess up the definition somewhere.

• Just wanted to add a comment to my own question: sometimes the MMA definition is used. I have seen it in the literature. With this definition $D^{J}_{mm'}$ is not daggered when rotating the cat-vector, which is logical. However, the Wiki definition is still much more conventional. – MsTais Dec 15 '17 at 16:33