Continuity statements and counterintuitive examples in connection with Weyl quantization

DOI10.1063/1.525882zbMath0541.44001OpenAlexW2044023329MaRDI QIDQ3327121

Ingrid Daubechies

Publication date: 1983

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

Full work available at URL: https://semanticscholar.org/paper/c3f2f556890eba29dc73f4c71661603b20cc584c

zbMATH Keywords

continuityWeyl quantizationcoherent statesWigner transformWeyl transformsymplectic Fourier transform

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory (81-01)

Related Items

Non-Abelian group quantization and quantum kinematic invariants of some noncompact Lie groups ⋮ The Wigner transform and the Wigner-poisson system ⋮ Heuristic approach to non-Abelian quantum kinematics and dynamics in configuration spacetime ⋮ Distributions of ℏ-positive type and applications ⋮ Quantum kinematics of the harmonic oscillator ⋮ Nonlinear partial differential equations on noncommutative Euclidean spaces ⋮ \(Qu^*\)-algebras and twisted product ⋮ The global indicator of classicality of an arbitrary \(N\)-level quantum system ⋮ Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra ⋮ Quantum Harmonic Analysis of the Density Matrix ⋮ Square Integrable Representations, An Invaluable Tool ⋮ On the averaged quantum dynamics by white-noise hamiltonians with and without dissipation ⋮ Modulation spaces and pseudodifferential operators

Cites Work

• The action option and a Feynman quantization of spinor fields in terms of ordinary \(C\)-numbers
• On the distributions corresponding to bounded operators in the Weyl quantization
• When is the Wigner quasi-probability density non-negative?
• Parity operator and quantization of \(\delta\)-functions
• Deformation theory and quantization. II: Physical applications
• Elementary properties of nested Hilbert spaces
• Sul comportamente asintotico dell'n -esimo polinomio di Laguerre nell'intorno dell'ascissa 4n
• On a Hilbert space of analytic functions and an associated integral transform part I
• The weyl calculus of pseudo-differential operators
• On the Quantum Correction For Thermodynamic Equilibrium
• Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
• Mathematical Aspects of the Weyl Correspondence
• Hilbert Spaces of Type S