Recent content by lennyleonard

Ok, I totally messed up-- I meant |a|\leq 1, a\neq 0. What about this mapping? Sorry for the inconvenience :) :) :)

Thank you for your kind answer lavinia! But I'm afraid I'm going to need a little more help to get to the bottom of this :) Is it now clear that i cannot take a\in\mathbb R/0, but what is I restrict to 1\leq |a|<\infty ? This gives indeed a homomorphism beween the fiber! I really cannot see how...

Thanks a lot pal, you have been very kind and helpful! cheers!

Thanks a lot Bill_K, now I see that the two ways of transformation are not mutually exclusive! I have taken some time to work to the bottom of this matter, but I cannot still set my mind at ease.. Can you be a little more specific on how the total transformation of O^a_{xy} looks like...

Thank you both for your quick and kind replies! Anyway I am still a bit confused.. So the correspondence is simply O_i=\lambda_{xy}O_{xy}=Tr(\lambda_i^T O) as you suggest? I still cannot verify the correspondences explicitly starting from Moreover the T_as above are already the su(3)...

Hi everyone! I would like to ask you a very basic question on the decomposition 3\otimes\bar 3=1\oplus 8 of su(3) representation. Suppose I have a tensor that transforms under the 8 representation (the adjoint rep), of the form O^{y}_{x} where upper index belongs to the $\bar 3$ rep and the...

Hi everyone! I would like to ask you some clarifications on an explicit example of local trivializations and transition functions of fibre bundles: namely on the [-1,1]\hookrightarrow E\rightarrow S^1 bundle (which I guess is the simplest possible example). Following Nakahara (chapter 9...

You are absolutely right Phinds! The truth is I've posted this in the algebra section but then i realized that this was the best section to post in. If tou tell me how to delete a post i'll be glad to do that. Sorry for the issue!

Hi everyone! I can't figure out why electromagnetism is defined a non integrable phase factor (or path dependent), referring to the element of the Lie group U1 to which it (the phase factor) belongs. Why it's said to be non-integrable? And, precisely, how do we specify a path for the...

Thanks a lot for your help fellas!

As you may guess from the title this question is about the covariant derivatives, more precisely about the difference between the usual covariant derivative, the one used in General Relativity defined by:\nabla_{e_{\mu}}=\left(\frac{\partial v^{\beta}} {\partial...

Your explanations have been extremely clarifying, sir. Thank you very very much!

You've been very kind to spend some of your time on my problem henry_m! I'm very thankful! But please, be patient enough to see if my conclusions are right: Basically the difference in the two method (aside for the derivations) is that the former is the "quick-straight to the result" one, which...

Thank you petr! I had this doubt when i saw the definition of "first variation" of a functional: according to the textbook i red (and to wikipedia: http://en.wikipedia.org/wiki/First_variation" ); taken a functional J(y) it's said that I need a function h to define the variaton of...

Hi everyone! Here's my problem: Let's suppose that we have a functional I[f,g]=\int{L(f,\dot{f},g,\dot{g},x)\,dx}. Is it right to say that the variation of I whit respect to g (thus taking g\;\rightarrow\;g+\delta g) is \delta I=\int{[L(f,\dot{f},g+\delta g,\dot{g}+\delta \dot...