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Aleolomorfo

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- Different sign in the combination of two ##\textbf{1/2}## isospins with opposite third component

**Summary:**Different sign in the combination of two ##\textbf{1/2}## isospins with opposite third component

Hello everybody!

I was doing an exercise regarding isospin and I noticed something from the Clebsch-Gordan coefficients that made me think.

For example, if I consider the combination between the two angular momenta ##|\textbf{1/2}, +1/2>## and ##|\textbf{1/2}, -1/2>##, in the Clebsch-Gordan table there are two possibilities. One in which ##I_z=+1/2## is put first and the second in which ##I_z=+1/2## is put after. I have attached the table and I have highlighted what I am saying inside a red circle.

The two combinations gives different coefficients, just for a sign.

My question is: what is the difference between combining ##|\textbf{1/2}, +1/2>## ##|\textbf{1/2}, -1/2>## and ##|\textbf{1/2}, -1/2>## ##|\textbf{1/2}, +1/2>##? Should not they be equal? From what comes the minus sign?

Thank you in advance!