The Resolvent Algebra: A New Approach to Canonical Quantum Systems

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dc.creatorBuchholz, Detlev
dc.creatorGrundling, Hendrik
dc.date2007-05-14
dc.date2008-04-03
dc.date.accessioned2026-07-07T09:29:46Z
dc.date.available2026-07-07T09:29:46Z
dc.descriptionThe standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C*-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C*-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples.
dc.description52 pages, no figures; v3: as to appear in Journal of Functional Analysis
dc.identifierhttps://arxiv.org/abs/0705.1988
dc.identifierhttp://arxiv.org/abs/0705.1988
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157906
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleThe Resolvent Algebra: A New Approach to Canonical Quantum Systems
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