title: Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions.
abstract: We show that the series product, which serves as an algebraic rule for connecting state-based input-output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.
authors.affiliation: Institute of Mathematics and Physics, Aberystwyth University, Ceredigion, UK.
authors.forename: D Gwion
authors.initials: DG
authors.lastname: Evans
authors.forename: John E
authors.initials: JE
authors.lastname: Gough
authors.forename: Matthew R
authors.initials: MR
authors.lastname: James