Recent content by flix

Thank you so much! I never really liked the covariant picture, although it looks very elegant. It always leads to me missing out basic things. I really have to dig into it now...

well yes, since applying the Euler Lagrange equation on the KG Lagrangian should produce the KG equation: EL: \frac{\partial L}{\partial \Phi} - \partial_{\mu} \left( \frac{\partial L}{\partial(\partial_{\mu} \Phi} \right) = 0 KG equation: (\square + m^2) \Phi(x, t) = 0

same source. the factors 1/2 are there throughout, and it certainly makes sense for the mass term where a factor 2 comes from differentiating. But where does the factor 2 come from when differentiating by \partial_{\mu} \Phi ?? Probably I miss out a very simple thing...

ok, quick and dirty and stupid question about calculation rules with 4 gradients: consider the Klein Gordon Lagrangian L_{KG} = \frac{1}{2} \partial_{\mu}\Phi\partial^{\mu} \Phi - \frac{1}{2} m^2 \Phi^2 . Why is \partial_{\mu} \left( \frac{\partial L_{KG}...

@samalkhaiat: yeah, well, this is exactly why I want to understand this, to motivate the Lagrangian .. ok, for all other still interested, I found a classical derivation. Of course my initial assumption was plain wrong, as pointed out by atyy: the potential energy of a string element does NOT...

yeah I don't get there, either. I'll have another go today and I will post any progress here. Damn you, classical mechanics!

damn, stupid mistake. of course I don't have to integrate the force over x, but over \Phi ! One gets: E(x) = \int\limits_0^{\Phi} \rho c^2 \frac{\partial^2 \Phi}{\partial x^2} \,d\Phi and this looks much more like it might ultimatel lead to victory if I can somehow find my old...

I see what you are heading at, still I don't get it mathematically. The true Force pulling the string back is: F(x) = T \, \frac{\partial ^2 \Phi}{\partial x^2} with T = \rho c^2 being the tension (pulling at the ends of that string segment tangentially). So the potential energy of that...

Hello, I know this has already been asked (unfortunately without answer)... learning once again for an exam (quantum field theory) I can't figure out a feature of a very central quantity: the total energy of a vibrating string. Let's start at the string (field) wave equation...

Ah ok I just found the (as expected: obvious) solution. As I stated I already showed that the integral vanishes for t_1 = t_2 and the integral is also Lorentz invariant. So I can transform without changing its value. Now when x_1 and x_2 are space-like separated I can always transform to a...

edit: where are my manners :) Thanks so much for helping me out so far! I see your comment is certainly going into the right direction, all I need now is my humble mind to catch on :) well I am working on it. The quantities in D(x_1, x_2) as I wrote it are 4 vectors. I know something about the...

The book suggests it should be possible without further calculations. I mean you can nicely show that for equal times the integral vanishes, and surely it must be possible to show that it vanishes in general, but somehow it must be possible to show in a very easy way that it is sufficient that...

[SOLVED] Quantum Field Theory: Field Operators and Lorentz invariance Hi there, I am currently working my way through a book an QFT (Aitchison/Hey) and am a bit stuck on an important step in the derivation of the Feynman Propagator. My problem is obviously that I am not a hard core expert...