Do Fermionic Creation and Annihilation Operators Commute?

[Niles]

Hi guys

The fermionic creating and annihiliations operators: Do they satisfy

$$c_{i,\sigma }^\dag c_{i,\sigma }^{} = - c_{i,\sigma }^{} c_{i,\sigma }^\dag$$

for some quantum number i and spin σ, i.e. do they commute?

 

[ansgar]

yes they satisfy that, but that is called ANTIcommute

 

[peteratcam]

$$c_{i,\sigma } c_{i,\sigma }^{\dag} = 1 - c_{i,\sigma }^{\dag} c_{i,\sigma }$$