Say I have a hamiltonian with fermion creation / annihilation operators like this:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum_{k_1,k_2,k_3,k_4} c_{k_1,\uparrow}^{\dagger} c_{k_2,\downarrow}^{\dagger} c_{k_3,\downarrow} c_{k_4,\uparrow} [/tex]

where the k's are momenta and the arrows indicate spin up / spin down. Can I commute operators for different spins? That is, does

[tex] c_{k_1,\uparrow}^{\dagger} c_{k_2,\downarrow}^{\dagger} = c_{k_2,\downarrow}^{\dagger} c_{k_1,\uparrow}^{\dagger} [/tex]

Or do I pick up a minus sign as usual? Thanks!

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# Do creation operators for different spins commute?

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