- #1
stone
- 41
- 0
For spin 1/2 particles, I know how to write the representations of the symmetry operators
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, let's 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.
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, let's 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.