Particle Spin and the Unitary Representations of the Poincaré Group

Sammanfattning

The unitary representations of the Poincaré group are of physical interest since this is how Poincaré invariance is implemented in quantum mechanics, which is required for compatibility with the special theory of relativity. In this thesis we review the algebraic structure of the Lorentz and Poincaré groups before moving onto classifying the (physical) unitary representations of the Poincaré group. We find that there are two types of representations that correspond to massive and massless particles. In the massive case we find that these particles must carry the internal degree of freedom of spin. On the other hand in the massless case we find that these particles must carry helicity.