I'm trying to show that the composition of two Lorentz boosts produces a boost and a rotation using the generators from the Lorentz Group. If →K denotes the Lorentz Boost generators and →S denotes the rotation generators then two successive Lorentz Boosts in the x- and then y-directions is given by e−ξyKye−ξxKx
How do I go on from here to prove the result is another boost and a rotation? I know I have to make use of the commutator [Ki,Kj]=−ϵijkSk
but I'm not sure how to proceed.
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