Self adjoint extensions satisfying the Weyl operator commutation relations

DOI10.1007/BF02797680zbMath0448.47012OpenAlexW1975726069MaRDI QIDQ1146861

Paul S. Muhly, Palle E. T. Jorgensen

Publication date: 1980

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02797680

zbMATH Keywords

quantum mechanicscommutation relationscharacteristic operator functionHeisenberg-Weyl relations

Mathematics Subject Classification ID

Subnormal operators, hyponormal operators, etc. (47B20) Commutators, derivations, elementary operators, etc. (47B47) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Equations involving linear operators, with operator unknowns (47A62) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (31)

On the Weyl algebras for systems with semibounded and bounded configuration space ⋮ Invariant dissipative operators on locally compact groups ⋮ Dissipative and nonunitary solutions of operator commutation relations ⋮ Reflexive \(^*\)-derivations and lattices of invariant subspaces of operator algebras associated with them ⋮ \(C^{*}\)-subalgebras generated by a single operator in \(B(H)\) ⋮ Ultra-weak time operators of Schrödinger operators ⋮ The orthogonal Lie algebra of operators: ideals and derivations ⋮ Time operators for quantum walks ⋮ On representations of groups and algebras in spaces with indefinite metric ⋮ Positive definite functions on the Heisenberg group ⋮ Extensions and index of Hermitian representations ⋮ Extensions of positive definite integral kernels on the Heisenberg group ⋮ Non-commutative moment problems ⋮ Off-diagonal terms in symmetric operators ⋮ Geometric construction of \(*\)-representations of the Weyl algebra with degree 2 ⋮ On the local operator commutation relations and extensions of locally defined positive definite functions on the Heisenberg group ⋮ Spectral theory for one-parameter groups of isometries ⋮ Hilbert spaces of martingales supporting certain substitution-dynamical systems ⋮ On action of diffeomorphisms of \(C^{\ast}\)-algebras on derivations ⋮ Existence of Smooth Solutions to the Classical Moment Problems ⋮ C * -subalgebras generated by partial isometries ⋮ Positive elements in the algebra of the quantum moment problem ⋮ On the Heisenberg commutation relation. II ⋮ A New Formula Relating Localisation Operators to Time Operators ⋮ Spectral theory of multiple intervals ⋮ On the Heisenberg commutation relation. I ⋮ Translation representations and scattering by two intervals ⋮ Representations of differential operators on a Lie group, and conditions for a Lie algebra of operators to generate a representation of the group ⋮ Dilations of symmetric operators shifted by a unitary group ⋮ On left invariant dissipative operators ⋮ Semigroups of measures in non-commutative harmonic analysis

Cites Work

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