Classifying the Unitary Irreducible Representations of the Euclidean 3 Group using Mackey Analysis

The Euclidean groups describe the symmetries of a flat spacetime endowed with a Euclidean, that is, always + metric. Quantum mechanical systems with Euclidean symmetry in d dimensions are Unitary Irreducible Representations (UIRs) of the d-dimensional Euclidean group. Classifying such representations are therefore of interest for understanding Euclidean dynamics. The Euclidean 3 group breaks down as a semi-direct product of SU(2) and R^3, where the action is rotational. The UIRs can be classified by Mackey Analysis. In this talk we will define the Euclidean 3 group Euc(3), introduce the method of Mackey and apply it to finding the UIRs of Euc(3).