On the Heisenberg commutation relation. II

DOI10.2977/prims/1195182446zbMath0557.47023OpenAlexW2073128339MaRDI QIDQ762443

Konrad Schmüdgen

Publication date: 1983

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195182446

zbMATH Keywords

unitary operatorsunbounded *-representationsself-adjoint extensionsanalytic vectorWeyl relationHeisenberg commutation relation on a common coreOp*-algebra

Mathematics Subject Classification ID

Algebras of unbounded operators; partial algebras of operators (47L60) Applications of operator algebras to the sciences (47L90) Linear symmetric and selfadjoint operators (unbounded) (47B25) Commutators, derivations, elementary operators, etc. (47B47) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (18)

Dissipative and nonunitary solutions of operator commutation relations ⋮ Unnamed Item ⋮ Completely positive conjugate-bilinear maps on partial *-algebras ⋮ Hilbert space representations of generalized canonical commutation relations ⋮ Ultra-weak time operators of Schrödinger operators ⋮ An unbounded generalization of Tomita's observable algebras ⋮ Operator representations of the real twisted canonical commutation relations ⋮ Momentum operators with gauge potentials, local quantization of magnetic flux, and representation of canonical commutation relations ⋮ Representations of the weak Weyl commutation relation ⋮ Perturbations of selfadjoint operators with point spectra by restrictions and selfadjoint extensions ⋮ Remarks on Infinite-Dimensional Representations of the Heisenberg Algebra ⋮ TIME OPERATORS OF A HAMILTONIAN WITH PURELY DISCRETE SPECTRUM ⋮ Construction of a Weyl representation from a weak Weyl representation of the canonical commutation relation ⋮ Necessary and sufficient conditions for a Hamiltonian with discrete eigenvalues to have time operators ⋮ On the uniqueness of weak Weyl representations of the canonical commutation relation ⋮ An unconventional canonical quantization of local scalar fields over quantum space-time ⋮ Canonical quantization on a doubly connected space and the Aharonov-Bohm phase ⋮ Weak commutation relations of unbounded operators and applications

Cites Work

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• Analytic vectors
• Classification of certain pairs of operators (P,Q) satisfying \([P,Q=- iId\)]
• Perturbations of selfadjoint operators with point spectra by restrictions and selfadjoint extensions
• Self adjoint extensions satisfying the Weyl operator commutation relations
• Self-adjoint algebras of unbounded operators
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Topological algebras of operators
• Selfadjoint operator extensions satisfying the Weyl commutation relations
• Two theorems about topologies on countably generatedOp*-algebras
• On the Relation $PQ -QP = -iI$.
• Analytic and Entire Vectors for Representations of Lie Groups

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