Recent content by faklif

I've kept studying and I think that the minus sign which appears is from \{\Psi_a(x),\Psi_b(y)\} = \delta(x-y)\delta_{ab}. What I don't understand is what happens at x=y with a=b? Don't I have to account for this as well since the sum is over all a and b and not limited in space?

Homework Statement I want to check that the QED lagrangian \mathcal{L}=-\frac{1}{4}F^{\alpha\beta}F_{\alpha\beta} + \bar\Psi(i\displaystyle{\not} D - m)\Psi where F^{\alpha\beta} = \partial^\alpha A^\beta - \partial^\beta A^\alpha, \ D^\mu = \partial^\mu - ieA^\mu is invariant under charge...

I've three things which I think help me, all closely related to repitition. 1. Do things fast first to get a general idea and then go back and do things properly, filling in the gaps of the first run through. 2. When solving problems I can sometimes see the point in sitting with the same...

Thanks a lot! Seems keeping things simple works here. It's really interesting to have to think about these kinds of problems though.

I'm using my summer vacation to try to improve my understanding of real analysis on my own but it seems it's not as easy when not having a teacher at hand so I've a small question. Homework Statement The problem concerns extending a De Morgan relation to more than two sets and then, if...

Thanks, I don't know what I was thinking. ;)

Homework Statement I have a sphere on top of another larger fixed sphere. The sphere on top rolls on the fixed one without sliding. The moving sphere is rolling and therefore has an angular velocity, it also moves giving it an angular velocity around the center of the fixed sphere. To calculate...

Hi and thank you! Now that I think some more about it (should have done that before spending the better part of the weekend :wink:, having to much spare time makes me stupid...) it makes sense. For a given a,b,c you'd still get the same implied summations. Thanks again for rescuing my monday!

Homework Statement The problem concerns how to transform a covariant differentiation. Using this formula for covariant differentiation and demanding that it is a (1,1) tensor: \nabla_cX^a=\partial_cX^a+\Gamma^a_{bc}X^b it should be proven that \Gamma'^a_{bc}=...

Thank you! \delta'^a_b=\frac{{\partial}x'^a}{{\partial}x^c}\frac{{\partial}x^d}{{\partial}x'^b}\delta^c_d=\frac{{\partial}x'^a}{{\partial}x^c}\frac{{\partial}x^c}{{\partial}x'^b}=\frac{{\partial}x'^a}{{\partial}x'^b}=\delta^a_b So that would do it? Two main things get me here. I...

Thanks for your reply! What looks most like a definition to me is: A contravariant tensor of rank 1 is a set of quantities, written X^a in the x^a coordinate system, associated with a point P, which transforms under a change of coordinates according to...

Homework Statement The problem straight out of the book reads: Prove that the Kronecker delta has the tensor character indicated. Prove also that it is a constant or numerical tensor, that is, it has the same components in all coordinate systems. Without a context the first sentence...

Thank you everyone!

Thanks a lot that does it! Also gives me another question and that is how to find that arcsinh(x)=x-x^3/3!+...? My thought of simply solving for t and then looking at what I got didn't really get me there. How can I do that substitution? I'm feeling very rusty here, I'm sorry.

Thanks for the reply! Using the first four terms of each of the expansions I end up with what looks like the some kind of opposite to what I want {T}\approx{t}(1+\frac{\alpha^2{t^2}}{6c^2}) I can't see that I can get where I want from this and I haven't used all information...