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...
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...
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...