Wigner Matrix or Wigner D-Matrix?

[TheDestroyer]

Hello guys,

I'm reading the attached article, and I found there the Wigner Matrix, the first equation in the second page... is that the Wigner D-Matrix? I really got lost in that. It doesn't look like the Wigner D-Matrix I see everywhere, and it's not the so-called random matrix... anyone knows what that really is? please explain!

Thank you for any efforts.

 

[dextercioby]

It's not the Wigner D-matrix from the representation theory of SU(2), but the matrix of the Wigner function from quantum transport equation.

 

[TheDestroyer]

Thank you for your reply.

Can that be found in some book? I don't know where to read about that.