Further Representations of the Canonical Commutation Relations

Details Further Representations of the Canonical Commutation Relations Further Representations of the Canonical Commutation Relations

2000-06-11

arxiv.org/abs/math-ph/0006011v1

Proc.Lond.Math.Soc.80:451-490,2000

Physics

Mathematical Physics

Scientific paper

10.1112/S0024611500012259

We construct a new class of representations of the canonical commutation relations, which generalizes previously known classes. We perturb the infinitesimal generator of the initial Fock representation (i.e. the free quantum field) by a function of the field which is square-integrable with respect to the associated Gaussian measure. We characterize which such perturbations lead to representations of the canonical commutation relations. We provide conditions entailing the irreducibility of such representations, show explicitly that our class of representations subsumes previously studied classes, and give necessary and sufficient conditions for our representations to be unitarily equivalent, resp. quasi-equivalent, with Fock, coherent or quasifree representations.

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