Representations of the Lorentz Group

Abstract

Having seen the importance in quantum mechanics of understanding the representations of the rotation group SO(3) and its double cover \(Spin(3)=SU(2)\), one would like to also understand the representations of the Lorentz group SO(3, 1) and its double cover \(Spin(3,1)=SL(2,\mathbf C)\). One difference from the SO(3) case is that all non-trivial finite dimensional irreducible representations of the Lorentz group are non-unitary (there are infinite dimensional unitary irreducible representations, of no known physical significance, which we will not discuss).