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(adsbygoogle = window.adsbygoogle || []).push({});

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

e.g.

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?

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# Difference in phase convention for Wigner d-function

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