Problem Set 3 Solutions Nabil Iqbal

Of this algebra really only the first line should be unfamiliar, as the second line simply says that Pμ and Kμ are vectors and the last line is just the Lorentz algebra SO(p, q). Now to put this into a more intuitive form we imagine that we are in a bigger space with two extra coordinates which we call −1 and 0 (the remaining coordinates are then 1...p+ q). Now consider the algebra defined by the following antisymmetric tensor generators Jab (where a, b include the two new coordinates and μ, ν run only over the original p+ q)