Demonstrate that the Bogoliubov quasiparticle creation and annihilation operators obey the anticommutators (left{alpha_{k}, alpha_{k^{prime}} ight}=left{alpha_{k}^{dagger}, alpha_{k^{prime}}^{dagger} ight}=0)

Demonstrate that the Bogoliubov quasiparticle creation and annihilation operators obey the anticommutators \(\left\{\alpha_{k}, \alpha_{k^{\prime}}\right\}=\left\{\alpha_{k}^{\dagger}, \alpha_{k^{\prime}}^{\dagger}\right\}=0\) and \(\left\{\alpha_{k}, \alpha_{k^{\prime}}^{\dagger}\right\}=\delta_{k k^{\prime}}\) given in Eq. (22.30), if the bare fermion operators satisfy the

fermionic anticommutator algebra.

Data from Eq. 22.30

Transcribed Image Text:

{ c, c}} = dij {c, c}} = [c,c; } = 0