Recent content by parton

Ok, now I understand. You are right. Indeed, it is related to the different pictures, I just needed to remember :) Thank you very much!

No, actually I already studied physics some time ago. But now when I read this text from Heisenberg (which is quite interesting to read even nowadays), I am not sure what he really means at this point. But is there really a connection between the different pictures and the...

Hi! I am a bit confused about something Heisenberg said about the wave-particle dualism. In his book about physics and philosophy he wrote: "The dualism between the two complementary pictures - waves and particles - is also clearly brought out in the flexibility of the mathematical scheme. The...

Hi! I have the following problem: A have a friend who is finishing her PhD and I wanted to give her a present. Altough I know her for more than 6 years, I have absolutely no idea what to give her. Here are a few things which could help to find an idea: - she will work outside physics, so...

OK, thanks a lot :smile:. This seems to work. But what I still not undestand is: Why can the result - \dfrac{1}{4 \pi^{2} x^{2}} be undestood as Cauchy's principal value?

Thank you for your hint, but somehow I don't see how that could help. If I make the substitution k' = i k I find: \begin{align} \int_{0}^{\infty} \mathrm{d}k & \left[ \mathrm{e}^{ik(x_{0}+r)} - \mathrm{e}^{-ik(x_{0}+r)} + \mathrm{e}^{-ik(x_{0}-r)} - \mathrm{e}^{ik(x_{0}-r)} \right] =...

Hi! I have encountered a little problem. I want to show that the explicit form of the Feynman propagator for massless scalar fields is given by: \begin{align} G_F(x) & = - \lim_{\epsilon \to +0} \int \dfrac{\mathrm{d}^{4}k}{(2 \pi)^{4}} \dfrac{1}{k^{2} + i \epsilon} \mathrm{e}^{- i k...

I want to determine the orbits of the proper orthochronous Lorentz group SO^{+}(1,3) . If I start with a time-like four-momentum p = (m, 0, 0, 0) with positive time-component p^{0} = m > 0 , the orbit of SO^{+}(1,3) in p is given by: \mathcal{O}(p) \equiv \lbrace \Lambda p...

Thanks again for your reply. Yes, your are right of course. But I did not say the opposite. I was just saying that if a Lie group is compact and connected every element of the group (and not only locally, i.e., in a neighborhood of the identity) can be expressed as exp(X), where X is an...

Thanks for your reply :smile: I think the usual notation is \mathcal{L}_{\uparrow}^{+} or SO^{+}(1,3) . In the latter case, the arrow is not necessary, because the 'S' already expresses the fact that the determinant is 1. The exponential map links the Lie group in a neighborhood of...

Hi! I was wondering why it is possible to write any proper orthochronous Lorentz transformation as an exponential of an element of its Lie-Algebra, i.e., \Lambda = \exp(X), where \Lambda \in SO^{+}(1,3) and X is an element of the Lie Algebra. I know that in case for compact...

Hi! I have a little problem. Consider a 4-fermion interaction (neglecting constant factors) of the form \overline{\psi_{a \mathrm{L}}} \gamma^{\lambda} \psi_{b \mathrm{L}} \overline{\psi_{c \mathrm{L}}} \gamma_{\lambda} \psi_{d \mathrm{L}} . I want to average this interaction over a...

Ok, Thanks!

Hi! I just need a "yes" or "no" answer. If i have to show that two lie algebras are isomorphic, is it sufficient to show that their generators fulfill the same commutation relations?

Ok, I should have somehting. (\delta'(\lambda x), f) = \dfrac{1}{\vert \lambda \vert} \left( \delta', f(x/\lambda) \right) = \dfrac{(-1)}{\vert \lambda \vert} \left( \delta, \partial [ f(x/\lambda) ]/ \partial x \right) = \dfrac{(-1)}{\lambda \vert \lambda \vert} \left( \delta, f'(x/\lambda)...