Distributions of ℏ-positive type and applications

DOI10.1063/1.528537zbMath0716.70023OpenAlexW1980582014MaRDI QIDQ3204103

Francis J. Narcowich

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1063/1.528537

zbMATH Keywords

Fourier transformsprobability measuresWeyl correspondencequantum Liouville equationsignal analysis(Schwartz) distributionscontinuous functions of positive typeStates in classical mechanicssymplectic Fourier transforms of Wigner distribution functions

Mathematics Subject Classification ID

Hamilton's equations (70H05) Axiomatic quantum field theory; operator algebras (81T05) Geometry and quantization, symplectic methods (81S10) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (12)

Newton’s identities and positivity of trace class integral operators ⋮ Coherent states expectation values as semiclassical trajectories ⋮ Features of Moyal trajectories ⋮ Partial traces and the geometry of entanglement: Sufficient conditions for the separability of Gaussian states ⋮ Mixed states with positive Wigner functions ⋮ Mixed quantum states with variable Planck constant ⋮ On a recent conjecture by Z. Van Herstraeten and N. J. Cerf for the quantum Wigner entropy ⋮ A refinement of the Robertson-Schrödinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions ⋮ Quantum Harmonic Analysis of the Density Matrix ⋮ Symplectic coarse-grained classical and semclassical evolution of subsystems: New theoretical approach ⋮ DEFORMATION QUANTIZATION AND WIGNER FUNCTIONS ⋮ Square Integrable Representations, An Invaluable Tool

Cites Work

• Quantum mechanics and partial differential equations
• The \(C^ *\)-algebras of a free Boson field
• \(C^ *\)-algèbres des systèmes canoniques. I
• An algebra of pseudodifferential operators and quantum mechanics in phase space
• Continuity statements and counterintuitive examples in connection with Weyl quantization
• Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation
• A Dyson-like expansion for solutions to the quantum Liouville equation
• The problem of moments in the phase-space formulation of quantum mechanics
• Algebras of distributions suitable for phase-space quantum mechanics. I
• Mathematical Aspects of the Weyl Correspondence
• Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group.

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