Lorentz generators

alphaone

Could somebody please show me the calculation which shows that the M_mu_nu representation of the Lorentz generators gives rise to a (1,0)+(0,0) representation? Thanks in advance

dextercioby

I don't think this is possible. [itex] M_{\mu\nu} [/itex] is different for every representation and the calculations are actually the other way around. The generators are computed by knowing how the spinors behave under restricted LT's.

alphaone

Thanks for the reply. I am sorry probably my notation is uncommon. When I said M_{\mu\nu} I meant the representation of the Lorentz generators when acting on a Lorentz 4-vector(so antisymmetric matrices, when all indices are raised). Also the way I learned it we started at differrent reps of the Lorentz generators and then afterwards defined the fields the transformation could act on and deduced its properties - seems to me to be some sort of chicken and egg problem. However I thought that it should be possible to compute that the vector representation is (1,0)+(0,0) as this is basically the spin of the object.

dextercioby

Actually the vector representation is (1/2,1/2). (1,0)+(0,0) is a reducibile representation and is made up of a self-dual 2-form and a scalar.