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In the Bogoliubov theory for the weakly interacting Bose gas, the Bogoliubov transformation from bosonic creation (annihilation) operators $\hat{a}_p^{(\dagger)}$ to the new set of creation (annihilation) operators $\hat{\alpha}_p^{(\dagger)}$ is defined via

$\hat{a}_p=u_p\hat{\alpha}_{p}-v_p\hat{\alpha}_{-p}^{\dagger}$ and $\hat{a}_{-p}^{\dagger}=u_p\hat{\alpha}_{-p}^{\dagger}-v_p\hat{\alpha}_{p}$.

I have looked various textbooks and lecture notes, and $u_p$ and $v_p$ are mostly assumed to be real. Why? Does this have some deeper meaning?

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No deep meaning. The only requirement on $u_p$ and $v_p$ is their normalisation condition: $$ |u_p|^2 - |v_p|^2 = 1.$$ For simplicity, and as usual in quantum mechanics, you just them to be real numbers.

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