Reduction of Lie--Jordan algebras: Quantum
arXiv:1309.4124 · doi:10.1393/ncc/i2013-11527-1
Abstract
In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties and the space of states. The reduced Lie--Jordan Banach algebra is characterized together with the Dirac states on the physical algebra of observables.