In the book "The oxford solid state basics", solutions book, question 6.2.a we can see the following derivation.
The marked statement says that a complex scalar and its conjugate can be treated as independent/separate variables when differentiating one with respect to the other (and thus the result will be 0)
Why is that?
Is there a physical logic behind it? Some approximation?
Is it mathematically correct?
Is more context needed?
There is a somewhat similar question here. The problem is that the question is articulated as a phenomenon of QFT which makes it much harder to understand the question and the answers. I believe that my question here is much more basic and I want to understand if it is a physical assumption or a complex analysis question (and thus belongs to math exchange).
