@antimony I don't think middle directly comes from the Greek mesos, but they're indeed cognates (supposed to come from the same root in proto Indo-European)
@DanielSank In v10 of Mathematica (the one I have) it means it couldn't evaluate the expression. It helpfully doesn't report any error - it just doesn't do anything. Though it isn't obvious why it can't evaluate an FT ...
Perhaps the simplest and most intuitive approach is to regularize the hard wall potential
$$V_0(x)~=~\left\{ \begin{array}{rcl} 0 &\text{for}& x<0 \cr\cr \infty &\text{for}& x>0\end{array}\right. $$
as
$$ \lim_{\varepsilon \to 0^+} V_{\varepsilon}(x) ~=~V_0(x).$$
For instance, one could cho...
Why does the open string state endowed with CP factors $\vert i j \rangle$ acquires a phase $exp(i(\theta_j-\theta_i))$? Specifically why the minus sign in between? This has to do with the fact that the two ends are oppositely charged under $U(1)$ but why is that so...is that because the string has to remain neutral?
@MoreAnonymous This is actually string theory which is not a QFT, though these things (like Wilson lines) are usually introduced at first in QFT, though it can make appearances in QM (like in the Aharonov Bohm effect).
I was trying to understand the Doppler effect across different mediums on the SE an came across the following question Doppler Effect and change in medium.
Though it's a homework question , I was attempting to understand the solution posted by the OP . Even after rereading and attempting it mysel...
When I open a link in stacksexchange, the math equations just can't show correctly. How do I fix it? (I've tried reinstalling Chrome, won't work. But things go well in Edge browser.)
For example when I open this link I see the following:
I usually don't study from one single book...because when i get stuck i tend to see other books...I started from Blundell's easy and lots-of-steps-given kinda book...Schwartz, Ashok Das, Srednicki and Peskin are really nice, and I use them very often
@ManasDogra it's just part of the definition of Chan-Paton factors - one end of the string transforms in the fundamental, the other in the antifundamental of the $\mathrm{U}(N)$.
in the original Chan-Paton setting of flux tubes between quarks that is very natural since the flux tube is between a quark and an anti-quark
in modern string theory it's just a random assumption :P
Depends on what your goals are, but there is a simple test with any (intro) book on Lie algebras, whether it discusses the Cartan classification or not
If qft is your focus, they almost certainly introduce everything one needs on the fly for the basics, but these notes or this book and similar sets of notes/books would be more useful than the above book
If I recall correctly the first one you mentioned required prior knowledge about groups, which I do not possess
This is why I was having a look at Naive Lie Theory, that looks much easier as a first attempt and it is not aimed to physicists, so mathematical understanding plays a bigger role. As per the book suggested by Bolbteppa (second link), I tend to avoid maths books aimed specifically for physicist at least on my first learning of the subject
Then I would recommend you read some algebra, otherwise dont worry too much about it. A nice easy book is: A book of abstract algebra by Pinter - just read the group theory part.
I dont see a way to learn about lie groups without knowing basic group theory