I understand that the fundamental representation of U(1) amounts to a multiplication by a phase factor, e.g. EM. I thought that when it is extended to higher dimensional representations, it would just become a phase factor times the identity matrix.
Can someone explain where the hypercharge comes into the U(1) generator matrices in SU(2)×U(1) model, e.g. Y=−(1/2)I in (2,−1/2) representation?
I don't quite understand where the "−1/2" comes from. Where do all these hypercharges come from?
What is the logic behind choosing a particular value like −1/2?
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