FULL REGULARITY FOR A C*-ALGEBRA OF THE CANONICAL COMMUTATION RELATIONS

DOI10.1142/S0129055X09003670zbMath1183.81088arXivmath/0605413MaRDI QIDQ5324590

Hendrik B. G. S. Grundling, Karl-Hermann Neeb

Publication date: 3 August 2009

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605413

zbMATH Keywords

\(C^*\)-algebragroup algebraWeyl algebracanonical commutation relationsquantum fieldsymplectic spaceregular representationhost algebra

Mathematics Subject Classification ID

Representations of general topological groups and semigroups (22A25) Axiomatic quantum field theory; operator algebras (81T05) Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Operator algebra methods applied to problems in quantum theory (81R15) Measure algebras on groups, semigroups, etc. (43A10) Character groups and dual objects (43A40)

Related Items (12)

The classical limit of a state on the Weyl algebra ⋮ Classical limits of gauge-invariant states and the choice of algebra for strict quantization ⋮ QCD on an infinite lattice ⋮ Quantization as a categorical equivalence ⋮ Reflection positivity and conformal symmetry ⋮ Why be regular? I. ⋮ Why be regular? II. ⋮ SOME C*-ALGEBRAS ASSOCIATED TO QUANTUM GAUGE THEORIES ⋮ Dynamics for QCD on an infinite lattice ⋮ Representations of \(^\ast\)-algebras by unbounded operators: C\(^\ast\)-hulls, local-global principle, and induction ⋮ Crossed products of \(C^\ast\)-algebras for singular actions ⋮ Erratum: "Full regularity for a C*-algebra of the canonical commutation relations"

Cites Work

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• Direct limit Lie groups and manifolds
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Twisted crossed products of C*-algebras
• C*-ALGEBRAS GENERATED BY UNBOUNDED ELEMENTS
• GENERALISING GROUP ALGEBRAS

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