Recent content by Hymne

Homework Statement Hello! I have been given a problem of ordinary differential equations to be solved in MATLAB by ode45. The equations are on a sheet but you can see what equations i put in. I did as the teacher instructed but MATLAB gives me a error message. Can you see what I misunderstood...

Hello! I've read some lie algebra in both group theory books and differential geometry books, and is confused about the different perspectives. The group theory approach is usually that the author introduce the generators and show that these fulfil the algebra. In differential geometry our...

Hello! I am trying to understand this subject but its not simple.. I will ask some question but if anybody wants to write a short introduction which explains my confusions in a continiuous text, that would be awesome as well. :) I think I got a good view of what our weigts are.. just...

Hello my friends! I'm trying to learn the meaning of young diagrams from Christoph Lüdelins physics751 (google it :) but I can't figure out what is happening in eqn 4.14. I understand why 4.13 are the possible p-cycles but how does eqn 4.14 apply to this S_5 example? (Sorry that I could not...

Thanks so much for the answers! You guys are a Redwood tree to hold on to when it gets to windy! Here comes some more questions that I struck upon: 1) In trying to get an geometric intuition for the group U(1) I wonder how the determinant of e^i\theta can be interpreted in terms of...

Thanks for the answers! Okey, so I understood it correctly. This is however what my intuition told me that the directproduct would look like. The xy-plane is a directprodukt of R with itself, and here we have the elements as a number pair (x, y) - i.e. we choose one element from each set...

Hello! I´m currently reading 'Groups, Representations and Physics' by H.F. Jones and I have drawn some conclusions that I would like to have confirmed + I have some questions. :) Conclusions: 1. An albelian group has always only one irrep. 2. The direct sum of two representations...

To summarize the previous post: It seems like we are setting a vector with infinitesimal components equal to one that is not infinitesimal.

Gah, this whole covector field chapter has made me confused.. Lee writes: df_p(X_p) = X_pf. Now, since X_p is a derivation I assume that I can write the RHS as: X_p f = v^i \frac{\partial f}{\partial x^i}(p), this is obviously vector for which the components are not of infinitesimal order...

Hmm, the sentence is taken from a chapter in field theory - so maybe it should be assumed that we are talking about the more relevant spaces in physics, e.g. minkowskispace. But the metric matrix is not choosen and the equations are in their general forms. There is not much to say.. really...

yeah thnx, I honestly don't know what I was thinking.. Do you mean it´s sounds suspicous or that you want more context? :)

I am referring to the following sentence (not found in Smiths book):

Thanks for the answer! One last question that popped up when I was reviewing though.. Smith writes that a pushforward fulfils: : (F_* X)(f) = X (f \circ F). Where: F: M \rightarrow N, X is in T_pM, (F_* X) is in T_{F(p)}N and f: N \rightarrow R However this means that the righthand side...

Aha! That makes much more sense. :) Lee has however a totally new way of picturing the covariant field than the way I described.. Still I haven't found any mathematical arguments why the one that I described is to prefer or even correct.

Hello Physicsforums! It is quite often that I find the geometrical visualization of a covector field as a field where the covector for each point bends along the manifold, M. That is to say it is "contained" in the surface - in contrast to the tangent field in which the vectors streches out...