Recent content by alle.fabbri

Hi all! I hope this is the right section to post such a question... I'm studying the theory of resolvent from the QM books by A. Messiah and I read in a footnote (page 713) that the norm of the resolvent satisfies \|R_A(z)\| = \lVert \frac{1}{A-zI} \rVert \ge \text{dist}(z,\sigma(A))^{-1}...

Hi guys! When we consider a system composed by two 1/2 spin particle we can label the 4 natural basis vector by the individual spin of each particle, i.e. |++>,|+->,... , or by the eigenvalues of the total spin S and its projection M. In the latter case we have again 4 basis vectors: a singlet...

Try to check on S. Carroll's book...I think there's something...

Thank you for the answer! I think I got the idea underlying your advice. Let me work it out. Since the simple pole of the function are the integers k on the real axis I get for them Res[f(z),k]=\underset{z\rightarrow k}{lim} \frac{\pi(z-k)}{tg(\pi z)} \frac{1}{(z-x)^2} = \frac{1}{(x-k)^2}...

Hi all! I found on a book of QFT in curved spacetime (Birrel and Davies, pag 53) the following identity cosec^2 \pi x = \frac{1}{sin^2 \pi x} = \pi^{-2} \sum_{k=-\infty}^{+\infty} \frac{1}{(x-k)^2} Can anyone help to derive it or give some reference to a book for the proof. I have no idea...

thanks all

Yep...

Hi all! Anyone knows where to find, online or on a book, the affine connection for the schwarzschild metric? Thanks

So the point is that when the metric has zero determinant is not invertible so we can't use it to define covariant vectors (crudely speaking: you can't lower tensor indices?), i.e. the elements of the dual space?

Hi all! I'm studying black holes and there's a point that I cannot understand. The book I'm reading is Modeling black hole evaporation, by Fabbri and Navarro Salas. The path is the following. After introducing the Schwarzschild metric ds^2 = \left(1 - \frac{2M}{r} \right) \ dt^2 - \left(1 -...

Mmh...i don't think it is so simple...i mean, a black hole is a physical entity (or, at least, we hope so...) while its white counterpart it's only a mathematical tool needed to cover the entire space-time manifold with the fewest possible number of charts. Indeed I think that Wheeler prooved...

Hi all! I think the keypoint of Thorne's statement can be found in the form of the Schwarzschild metric ds_S^{2} = \left(1-\frac{2M}{r} \right) dt^2 - \left(1-\frac{2M}{r} \right)^{-1} dr^2 - r^2 d \Omega^2 as you can see at the event orizon, located at r_S = 2 M the metric becomes ill...

I cannot find a definition of compactness for a group. Do you have one in mind? I mean that I usually try to establish a connection between a new mathematical concept or idea and the concepts I already have. The underlying motivation, in my opinion, is to find some path, some mechanics...

so this an example of the fact that O(V) is "bigger" than exp(t X) with X in o(V). I guess this is true in general, for every Lie Group, since the assumption we make on a group to make it a Lie one are only local. A question arise: are there lie groups that coincides with the exponential map of...

so when we look to O(V) as a Lie Group we are not able to describe reflections?