- #1
metapuff
- 53
- 6
Say I have a hamiltonian with fermion creation / annihilation operators like this:
[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!
[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!