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I try to know more about Bogoliubov transformation. I try to find some material to help me understand the transformation more. Most of the material I found are lack of physical explanation for me. Most of the many-body text book(Fetter and Flensberg) only try to convince me that the transformation can simplify the Hamiltonian and eliminate the cross terms. And we can diagonalize the many-body Hamiltonian as quadratic Hamiltonian. What I want to know is about the physical picture of this kind of transformation.

Also, I am confused about the phase term in the wikipedia

[tex]u=e^{i\theta}\cosh r[/tex]

I feel the phase term should mean something, which I do not find any reference about the phase factor.

Can anybody explain/(discuss about) what is Bogoliubov transformation and what is the meaning of the phase factor?Thanks very much. :)