2004/09/23 by T. Digernes, V. S. Varadarajan · 1 citation
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.MP #msc:81R99 #msc:20K10 #msc:20K35
published as "Infinite Dimensional Analysis, Quantum Probability and Related Topics", Volume 7, no. 4, December 2004, 527-546. · 14 pages, 1 figure. To be published in "Infinite Dimensional Analysis, Quantum Probability and Related Topics" (IDAQP). Added 2 references
arxiv created 2004/09/23 · arxiv updated 2009/12/01
In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. 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" of the irreducible representation exhibits a fermionic structure. This will be the case, for instance, in a quantum mechanical model based on the 2-adic numbers with a suitably chosen isotropic subgroup. The formulation in terms of Heisenberg groups allows a uniform treatment of p-adic quantum systems for all primes p, and includes the possibility of treating adelic systems.