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mpham26uchicago / scaling-train

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Can I rederive the magic basis through the Lie algebra homomorphism of su(2) ⊗ su(2) and so(4) #2

Open mpham26uchicago opened 1 year ago

mpham26uchicago commented 1 year ago

Two decomposition is isomorphic if $P\ell_iP^\dagger$ and $Pm_iP^\dagger$. Can I rederive the magic basis?

Now that I have the kroncker sum representation of $\mathfrak{su}(2) \otimes \mathfrak{su}(2)$. Maybe this shouldn't be too difficult...

mpham26uchicago commented 1 year ago

if you look at the magic basis adjoint action on the basis $\mathfrak{su}(2) \otimes \mathfrak{su}(2)$ you can see that it maps exactly to so(4). Now the conjugate(B) business that Tucci does I have no idea what that’s about. So maybe look at this when I have time