Little Group Method

The little group method, or Mackey theory as it is known to Mathematicians, is a way of constructing unitary representations of semi-direct products $G= K\ltimes T$, for $T$ abelian. Physically such unitary irreps should correspond to elementary particles in the case where $G$ is the double cover of the Poincaré group $G = SL_2(\mathbb{C}) \ltimes \mathbb{R}^4$. We will explain the general theory and how the field equations such as the Klein-Gordon or Dirac equation arise from this general framework. Time permitting or in a future talk we will explain how this extends in the supersymmetric case.