Unitary Representations of Super Lie Groups and Applications to the Classification and Multiplet Structure of Super Particles

Abstract

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincaré groups in arbitrary dimension and signature. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.