Some phenomena in the vacuum sector of an unconventional quantum system

Abstract: We study irreducible models for Heisenberg groups based on compact maximal isotropic subgroups. It is shown that if the Heisenberg group is 2-regular, but the subgroup is not, the "vacuum sector" exhibits a fermionic structure. This will be the case, for instance, in a quantum mechanical model based on the 2-adic numbers, with the 2-adic integers as isotropic subgroup.