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seen Feb 5 at 18:19

Jul
16
comment splitting spin representation when reducible
This is the construction of the full spin representation. I have no trouble following the construction in the link but this rep is reducible so there should be two irreps each consisting of 2x2 matrices...it's these 2x2 matrices that I'm after. Similarly for so(8,C) the full spin rep as constructed in the link is 16-dimensional. I'm looking for the two 8 dim irreps that this splits to...so two sets of 8x8 matrices..
Jul
15
asked splitting spin representation when reducible
Feb
1
awarded  Supporter
Jan
22
comment Wave functions for three identical fermions
It's too confusing to try to see how the L and S parts fit within the individual J ireps (to me at least). Same goes for trying to build things up with symmetrized and anti-symmetrized parts. Both these approaches do not scale to more complicated problems...
Jan
22
awarded  Teacher
Jan
22
comment Wave functions for three identical fermions
I don't think you can think of the j=5/2 state as being with L_{tot}=2, S_{tot}=1/2. An SU(2) irep is completely determined by a single label (here it's j). L and S are not necessarily conserved...
Jan
22
comment Wave functions for three identical fermions
I do not have these books so I can't comment on how they construct the basis for these ireps. In the past I saw many "add hoc" ways of combining symmetric and antisymmetric parts ...(for example in the construction of the proton spin 1/2 wavefunction from quarks with spin). What they have is probably ok, but choosing a basis always has more degrees of freedom than knowing how the space decomposes under the group.
Jan
22
answered Wave functions for three identical fermions