Recent content by DivergentMind

right, this is what i meant yes, this is the same problem i was facing. i tried to demonstrate it for specific indices, in my first post. i think it comes down to how we multiply one J by the other Edit: if we multiply J's as matrices, then you are right and there is probably something wrong...

i think dexter is implying that the J's are tensors, not matrices, and therefore the product of two Js is their contractions, and hence it is ok that one of the contracted indices is up and one is down (for otherwise, you cannot sum them) the answer to this is at the last line of my first...

OK, changed this to [J^{01},J^{12}]_{\alpha\beta} =(J^{01})_{\alpha\gamma}(J^{12})^{\gamma}_{\beta} -(J^{12})_{\alpha}^{\gamma}(J^{01})_{\gamma\beta} =(J^{01})_{\alpha\gamma}g^{\gamma\delta}(J^{12})_{\delta\beta} -(J^{12})_{\alpha\delta}g^{\delta\gamma}(J^{01})_{\\gamma\beta} and this...

I am trying to show that (for 4x4 matrices) the representation given by equation 3.18 (Peskin and Schroeder, page 39): (J^{\mu\nu})_{\alpha\beta} =i(\delta^{\mu}_{\alpha}\delta^{\nu}_{\beta}-\delta^{\mu}_{\beta}\delta^{\nu}_{\alpha}) implies the commutation relations in 3.17...