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[tex]R2=\sigma_1 \otimes\tau_3[\tex]

with "In the above, sigma acts in the spin basis and tau acts in the basis of P1+ and P2− subbands"

What does this product look like? Is it really a kronecker/direct product of the two matrices? I'm confused because they work in different bases. Or can I just do the kronecker product, resulting in i times:

0 0 1 0

0 0 0 -1

1 0 0 0

0 -1 0 0

In the appendix, gamma matrices are also defined in a similar way.

Can anyone point me in the right direction or give some insight on this? Thanks