Polarized States on the Weyl Algebra

  • Paul Lee Robinson

    University of Florida, Gainesville, USA

Abstract

A state on the Weyl algebra over a real symplectic vector space is polarized when the vectors for which the absolute value of on the corresponding Weyl generator is unity constitute a maximal -integral additive subgroup of ; such a state is necessarily pure, but has inseparable carrier space and is not regular. We determine fundamental properties of such states: in particular, we decide precisely when the GNS representations associated to a pair of polarized states are unitarily equivalent and decide precisely when a given symplectic automorphism is unitarily implemented in the GNS representation associated to a given polarized state.

Cite this article

Paul Lee Robinson, Polarized States on the Weyl Algebra. Publ. Res. Inst. Math. Sci. 39 (2003), no. 3, pp. 415–434

DOI 10.4171/PRIMS/39.3.1