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Hey lchigo449, thank you very much. So for every complex semi-simple Lie algebra there is a real compact Lie group whose complexification is the semi-simple Lie algebra. This is probably a basic fact, but as a Physicist I am struggling to find the relevant knowledge of this subject (I...

If the charts of your atlas map into R^n the manifold is real, if they map intor C^n it is complex.

Hello mathwonk, thank you for your answer. Unfortunately this argument is a bit too abstract for me. However, if this means that the statement is indeed true I will try to find a more elementary proof. If I fail I will ask for help in the Homework & Courseworks forum section.

Hello everybody, in Schwartz' QFT book it says (p. 483 - 484) In Problem 25.3 this is repeated asking the reader for a proof. I wonder though if this is really true. I know this can be proven for Lie algebras of compact Lie groups (or to be precise, every representation is equivalent to a...

If you want to put Ubuntu on your machine I advise you to buy one that uses a graphic card by intel, as they are supported with open source drivers. I especially advise NOT to use a hybrid solution like Nvidia Optimus, it still gives me problems on my notebook.

Don't fixate on the exact meaning of the word irrational, then it will make sense ;).

That's interesting and answers all of my questions so far. Thanks.

This was clear to me. Actually, the book does not use the notation where you write differences, but I thought to people who know affine spaces this notation is clear. Later I explicitely mentioned that (\varphi(\lambda + \epsilon) - \varphi(\lambda)) \in E , where E is the underlying vector...

Hi, thanks for your answer. Not sure if I understood you correctly. But to define the "standard topology" on \mathscr{E} I still have to choose an origin and a basis, right? So this would amount to the same thing like I said before:

Hello everybody, I'm currently reading the book Special Relativity in General Frames by Gourgoulhon. There, Minkowski Spacetime is introduced as an affine space \mathscr{E} over \mathbb{R} with a bilinear form g on the underlying vector space E that is symmetric, nondegenerate an has signature...

There is a reason why I posted it in the classical physics section. The books starts with the "wrong"/classical argument. That's also why in my first post it says "Classically, a box of size L supports...". And that's probably also the reason why I thought of rigid boundary conditions, because...

The solution is that he uses PBCs: http://quantum-field-theory-and-the-standard-model.1112349.n5.nabble.com/Blackbody-radiation-td12.html By the way I think it's really great of Prof. Schwartz that he has created a forum where he answers questions about his book (he encourages other people to...

Hello, in Schwartz's QFT-book it says that: "Classically, a box of size L supports standing electromagnetic waves with angular frequencies \omega_n = \frac{2\pi}{L}\left|\vec{n}\right|c (...)" I wonder if the factor 2 is really correct, I only get this factor 2 if I suppose that eg. for...