On the superselection sectors of fermions

Abstract

We classify elementary particles according to their behaviour under the action of the full inhomogeneous Lorentz group. For fundamental fermions, this approach leads us to delineate fermions into eight basic families or `types', corresponding to the eight simply connected double covering groups of the inhomogeneous Lorentz group (the `pin' groups). Given this classification, it is natural to ask whether or not fermion type determines a superselection rule. It is also important to determine what observable effects fermion type might have; for example, can the type of a given fermion be determined by laboratory experiments? We address these questions by arguing that if multiple fermion types really did occur in nature, then it would be mathematically equivalent and also much simpler to think of the different types as being different states of a {\it single} particle, which would be a particle which lived in the direct sum of Hilbert spaces associated with the different particle types. In the language of group theory, these are pinor supermultiplets. We discuss the possible experimental ramifications of this proposal. In particular, following work of J. Giesen, we show that the symmetries of the electric dipole moment of a particle would be definitely affected by this proposal. In fact, we show that it would be possible to use the electric dipole moment of a particle to determine the type. We also present an argument that M-theory may provide the mechanism which selects a {\it unique} pin bundle.