For spin 1/2 particles, I know how to write the representations of the symmetry operators(adsbygoogle = window.adsbygoogle || []).push({});

for instance [tex] T=i\sigma^{y}K [/tex] (time reversal operator)

[tex] C_{3}=exp(i(\pi/3)\sigma^{z}) [/tex] (three fold rotation symmetry) etc.

My question is how do we generalize this to, lets say, a basis of four component spinor with spins localized on two sites [tex]a [/tex] and [tex]b [/tex]

[tex](|a, up>, |a, down>, |b, up>, |b, down>)^{T}[/tex]

Is it a direct product [tex] i\sigma^{y}K \otimes i\sigma^{y}K[/tex]

Or [tex] i\sigma^{y}K \otimes I_{2 \times 2}[/tex]

Or is it something else?

It would be wonderful if you could point to any references.

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# Representations of Symmetry Operators

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