Recent content by Petraa

If I play with the indexs, lowering them etc. I just walk in circles. For example I get...

What I am trying to prove is that the commutator of the operator W^2 constructed from the Pauli-Lubanski pseudo vector is a Casimir operator for the poincare group. The whole commutator [W^2,M_ij] splits up into two parts, my textbook says that the first part should be zero and I've revised...

Yes, this is exactly the part that I do not understand. I thought that this procedure was incorrect... M is antisymmetric so M_{ij}=-M_{ji} I guess that M_{\thinspace\thinspace j}^{i}=-M_{\thinspace\thinspace i}^{j}...

I know what are trying to suggest me but I've tried that and I don't see why it should cancel. I feel so stupid right now :P. For example...

I think its M_{\nu\alpha}=g_{\nu\gamma}M_{\thinspace\thinspace\alpha}^{\gamma};M_{\thinspace\thinspace\alpha}^{\nu}=g^{\nu\gamma}M_{\gamma\alpha}

Yes with the metric. I've done it to get to this last result. Do you mean things like ... A^{i}=g^{ij}A_{j};A_{i}=g_{ij}A^{j};g^{ij}g_{ib}=g_{\thinspace\thinspace b}^{j}=\delta_{b}^{j} and this sort of stuff ?

The expression is...

M is total antisymetric. M are the generators of the lorentz group. The index order does matter but I have written it too fast in tex.

Thank you for your fast response. The problem is that this thing should be zero ... if it is not zero then there must be an error in the previous calculations. Is A=0 ? And why?

I'm not sure if this step on my calculation is correct or not...

Yes, indeed I'm using the Minkowski metric. The part where I have problems, as I just realized right now, is the difference between \partial_{\alpha}x_{\nu} \partial_{\rho}x^{\alpha} \partial^{\rho}x_{\alpha} \partial^{\rho}x^{\alpha} If you know any book for dummies like me where this topic is...

So basically \partial_{\rho}x_{\nu}=\partial_{\rho}g_{v\alpha}x^{\alpha}=g_{v\alpha}\partial_{\rho}x^{\alpha}=g_{v\alpha}\delta_{\rho}^{\alpha}=g_{\nu\rho}=g_{\rho\nu} Any mistake ?

@Orodruin Can you develop it a little more pls ? Because I have problems with this little quibbling of index notation and such

Homework Statement Given a Poincaré transformation, Lorentz+translation, I have to find the Poincaré generators in the scalar field representation and then prove that the commutation relations. I've done the first part but I can't prove the commutation relations. Homework Equations...

T^{\mu\nu}=-F^{\mu\nu}\partial^{\nu}A_{\rho}+\frac{1}{4}F^{2}g^{\mu\nu} And now? How I relate this to the momentum and total angular momentum operators ?