Recent content by ZuperPosition

Ah yes, you are right it might be much more fruitful to define the electromagnetic field tensor using the vector potential. I got a bit distracted as some of the literature seems to want to define the electromagnetic fields on Minkowski space before defining the electromagnetic field tensor. In...

Hello, In the sources I have looked into (textbooks and articles on differential geometry), I have not found any abstract definition of the electromagnetic fields. It seems that at most the electric field is defined as $$\bf{E}(t,\bf{x}) = \frac{1}{4\pi \epsilon_0} \int \rho(t,\bf{x}')...

Oh, thank you so much! This definitely helps!

Sorry, yes I wrote incorrectly, what I meant was $$\frac{d}{dz}\sin^{-1}(z) = \frac{1}{(1-z^2)^{1/2}}$$ for all ##z##in ##\mathbb{C}^*\backslash\{1,-1\}##. Another way to restate the question is: Are there any branch cut such that ##sin^{-1}(z)## is holomorphic (simultaneously as being single...

Thank you! Yes, I agree with what you are saying. So is it just sloppy notation by the book? That is, what they really want to say is that for some choice of branch cut the derivative is $$\frac{d}{dz}\sin^{-1}(z) = -i \log(iz + (1-z^2)^{1/2})$$ for all ##z \in \mathbb{C}^*\backslash \{1,-1\}##...

Homework Statement Our textbook, Fundamentals of Complex Analysis, (...) by Saff Snider says on page 135 that by choosing some suitable branch for the square root and the logarithm then one can show that any such branch satisfies the equation below. The homework/task is to find all such branch...