Recent content by teddd

By the way, since the question has actually changed should I open a new post??

That was my first guess. But can you explain me the following issue then? The spin angular momentum S^{\mu\lambda\kappa} is defined to be S^{\mu\lambda\kappa}=-i\frac{\delta\mathcal{L}}{\delta\partial_\mu u_A}(S^{\lambda\kappa})_{AB}u_Bwhere S^{\lambda\kappa}=\frac{i}{4}[\gamma^\lambda...

Hi there, I'm having a problem calculating the energy momentum tensor for the dirac spinor \psi (x) =\left(\begin{align}\psi_{L1}\\ \psi_{L2}\\\psi_{R1}\\ \psi_{R2}\end{align}\right)(free theory). So, with the dirac lagrangian \mathcal{L}=i\bar{\psi}\gamma^\mu\partial_\mu\psi-m\bar{\psi}\psiin...

Well, that is a functional derivative, being \partial_\mu \phi a function!

Hi guys, can you help me with this? I'm supposed to calculate the energy momentum for the classic Maxwell Lagrangian, \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} , where F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu with the well known formula: T^{\sigma\rho}=\frac{\delta\mathcal{L}}{\delta...

So it's on an improper use of the term representation I've been struggling upon! But another thing then: When we compose two right (left) weyl spinor to get something that transforms as a 4-vector, namely by doing...

Ok, that seems to clarify most of my problem on the reason of using SL(2,C). But I'm still stuck on the representation thing. I just cannot solve that. For example, the group SO(3) can be represented by 3x3 orthgonal matrices, which act on 3-dimensional vectors belonging to a vector...

OK, that's reassuring, thanks Bill_K, but why then i do read everywhere that the the spinor is a (0,1/2) representation of the Lorentz group? (I'm reading the pages you suggested me vanhees71...)

Hi guys! I still have problem clearing once and for all my doubt on the spinor representation. Sorry, but i just cannot catch it. 1) ----- Take a left handed spinor, \chi_L. Now, i know it transforms according to the Lorentz group, but why do i have to take the \Lambda_L matrices belonging...

Ok, so a left/right spinor is an element of a tensor product of linear spaces, precisely two of them, one for each component of the spinor itself. The matricies under which they transform are obtained from a mapping from the SL(2,C) group. But again, what is the representation matrix...

This makes sense. But it's like choosing a basis in a hilbert space, and to express any operator in function of it. But still, the operator remains the operator, and it acts on elements of the Hilbert space itelf! It's quite strange: the matrices of SL(2,C) act on spinors, how can they be...

Thanks for the pics dextercioby, but i don't know the notation you use (as well as the language) The thing that confuses me is that i know that the \tau_{mn} are the representation of the lorentz group, but i cannot see them as spinors/vectors! The spinors are the things that...

Thanks for the answers fellas, but I'm going to need some extra help here! I still have a hard time figuring out what is \tau_{mn}. I mean, should i see it as a regular matrix or instead as an element like \tau_{mn}=\left(\begin{align}\psi_1\\\psi_2\\...\\\psi_{m+n}\end{align}\right)? Reading...

Hi guys! I'm having some problems in understanding the direct products of representation in group theory. For example, take two right weyl spinors. We can then write\tau_{0\frac{1}{2}}\otimes\tau_{0\frac{1}{2}}=\tau_{00}\oplus\tau_{01} Now they make me see that...

Ok, that makes sense. But, as a last thing, can you explain why in question 3) ? I'm still wondering what proprieties must have a set of coordinates to be canonical coordinates Thanks a lot fellas!