Difference in phase convention for Wigner d-function

  1. I am looking for a way to connect the Condon-Shortley-Wigner to the Edmonds phase convention. Specifically I am writing a program to compute Wigner-d matrix coefficients

    From tabulated values (e.g. even Wikipedia) d^1/2_{1/2,-1/2}=(-1)^{-1/2-1/2}d^1/2_{-1/2,1/2}=-sin(theta/2)

    So d^1/2_{-1/2,1/2}=sin(theta/2)

    But from Edmonds, eq. 4.1.27 with j=1/2,m=-1/2 this should have a - sign
    d^j_{mj}=(-1)^{j-m}[(2j)!/((j+m)!(j-m)!]^{1/2} [cos(theta/2)]^{j+m} [sin(theta/2)]^{j-m}

    i.e. j=1/2, m=-1/2,j+m=0,j-m=1

    - sqrt(1!/(0! 1!)) [cos(theta/2)]^0 [sin(theta/2)]^1, i.e. the sign is off

    Is this an Edmonds typo or some different phase convention?
  2. jcsd
  3. Greg Bernhardt

    Staff: Admin

    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
  4. Yes, Edmonds has a typo. There should be no (-1)**(j-m) there.
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