Recent content by vega12

I am currently working with Lie algebras and my research requires me to have matrix representations for any given Lie algebra and highest weight. I solved this problem with a program for cases where all weights in a representation have multiplicity 1 by finding how E_\alpha acts on each node of...

The author of that study has actually posted in the comments here: http://www.icarusinterstellar.org/daydreaming-beyond-the-solar-system-with-warp-field-mechanics/. Looks like it is not published at the moment, so we can't see the details of the analysis. This also says how he came up with a...

My apologizes for not making my question as clear as it should have been. All the systems of equations I am working with are of the form: \frac{d X_i}{dt} = F_i(\mathbf{X)} So when I say that a solution diverges, I mean that given a set of initial conditions, the solution will diverge...

My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for...

I am very sorry for bumping my own thread with a double post. If it turns out that I cannot get a response here, could someone perhaps recommend a more appropriate subforum for me to post in? Would "general math" be more promising? Thanks.

I am currently trying to up my understanding of Lie algebras as the brief introductions I have had from various QFT textbooks feels insufficient, but have been stuck on one small point for a couple days now. I am reading through the lecture notes / book by Robert Cahn found here...

Well, sorry for the double post but I wanted to try one more time to see what you think about field derivatives in the interaction terms. After pressing on without knowing in detail (only vaguely) how the momentum terms crop up in the Feynman rules, I eventually got to the section on...

Hello, first of all thanks to Patrick for the nice explanation. I was struggling with this today also, but couldn't quite get it to work out. I tried to go back to square one and show how if one does perturbation theory about the rescaled Lagrangian those counter-terms would show up in the...

Wow, I spent quite some time searching the net and here and couldn't find that thread. My apologizes as it seems my question was answered there quite well. I was even finally able to locate the theorem on wikipedia: http://en.wikipedia.org/wiki/Sokhatsky%E2%80%93Weierstrass_theorem" . It even...

Thanks for the quick reply. I'm still unsure how exactly I can arrive at that specific relation, but at least I now know what it means so can understand how to use it. Could you give me an idea how I would go about showing it? Upon getting your response I decided to see if I can calculate...

Right now, I'm self-studying from J. J. Sakurai's book Modern Quantum Mechanics. In section 7.3, Optical Theorem, there is one step in the proof that he uses that escapes me. His proof involves using the transition operator T defined as: V \mid\psi^{(+)} \rangle = T \mid\phi \rangle \\...