Mathematical Aspects of the Weyl Correspondence
From MaRDI portal
Publication:5515298
DOI10.1063/1.1704817zbMath0139.45903OpenAlexW1981406915MaRDI QIDQ5515298
Publication date: 1966
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.1704817
Related Items (80)
Décomposition spectrale dans des algèbres munie d'un star-produit. (Spectral decomposition of an algebra equipped with a star product) ⋮ Mean Ergodic Theorems in Quantum Mechanics ⋮ Quantization in polar coordinates and the phase operator ⋮ The Wigner transform and the Wigner-poisson system ⋮ On Hansen's version of spectral theory and the Moyal product ⋮ Weyl quantization and star products ⋮ The Moyal representation for spin ⋮ Introducing groups into quantum theory (1926--1930) ⋮ Wigner-Ville distribution function in the framework of linear canonical transform ⋮ Weyl transformations on manifolds I. Definitions and isomorphism theorems ⋮ Distributions of ℏ-positive type and applications ⋮ Singular values of compact pseudodifferential operators ⋮ On informational completeness of covariant localization observables and Wigner coefficients ⋮ The affine Wigner distribution ⋮ Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile ⋮ A Dyson-like expansion for solutions to the quantum Liouville equation ⋮ \(C^*\)-algebras, \(H^*\)-algebras and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups ⋮ Weyl transforms associated with Dunkl wavelet transform ⋮ Asymptotic expansions of solutions to the heat equations with initial value in the dual of Gelfand-Shilov spaces ⋮ Exact equations for smoothed Wigner transforms and homogenization of wave propagation ⋮ On the distributions corresponding to bounded operators in the Weyl quantization ⋮ Spectral deviation of concentration operators for the short-time Fourier transform ⋮ \(Qu^*\)-algebras and twisted product ⋮ The problem of moments in the phase-space formulation of quantum mechanics ⋮ Function spaces and classes of pseudodifferential operators ⋮ Algebras of distributions suitable for phase-space quantum mechanics. I ⋮ Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra ⋮ Operator deformations in quantum measurement theory ⋮ Unnamed Item ⋮ Coherent states, inverse mapping formula for Weyl transformations and application to equations of KdV type ⋮ Fundamental physics ⋮ Weyl transforms associated with the Heisenberg group ⋮ On the representation of quantum mechanics on phase space ⋮ From the attempt of certain classical reformulations of quantum mechanics to quasi-probability representations ⋮ Continuity statements and counterintuitive examples in connection with Weyl quantization ⋮ The Weyl transform of distributions ⋮ Mixed-state localization operators: Cohen's class and trace class operators ⋮ On asymptotic expansions of twisted products ⋮ Non-trivial 1d and 2d Segal–Bargmann transforms ⋮ Optimal quantum measurements ⋮ Weyl transforms and a degenerate elliptic partial differential equation ⋮ Statistical decision theory for quantum systems ⋮ Wigner measures in noncommutative quantum mechanics ⋮ Canonical Fourier transforms ⋮ Gauge transformations and normal states of the CCR ⋮ Weyl transforms on the upper half plane ⋮ When is the Wigner quasi-probability density non-negative? ⋮ An evolution equation in phase space and the Weyl correspondence ⋮ Heat flow, BMO, and the compactness of Toeplitz operators ⋮ Parity operator and quantization of \(\delta\)-functions ⋮ Pseudodifferential operators on modulation spaces ⋮ Generalized Weyl transformation ⋮ Weyl transforms and the products of two wavelet multiplier operators on locally compact abelian topological groups ⋮ Aspects of the quantum-classical connection based on statistical maps ⋮ An algebra of pseudodifferential operators and the asymptotics of quantum mechanics ⋮ Quantum statistical mechanics on stochastic phase space ⋮ Translation-invariant traces and Fourier analysis on multiplier representation of vector groups ⋮ Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory ⋮ The phase-space approach to time evolution of quantum states in confined systems: the spectral split-operator method ⋮ Weyl transforms associated with the Hankel transform in Clifford analysis ⋮ An algebra of pseudodifferential operators and quantum mechanics in phase space ⋮ Average sampling in certain subspaces of Hilbert-Schmidt operators on \(L^2(\mathbb{R}^d)\) ⋮ Wiener measures for path integrals with affine kinematic variables ⋮ Affine quantum harmonic analysis ⋮ Unnamed Item ⋮ Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators ⋮ The multiplicative Weyl functional calculus ⋮ On the averaged quantum dynamics by white-noise hamiltonians with and without dissipation ⋮ Trace ideals for pseudo-differential operators and their commutators with symbols in \(\alpha \)-modulation spaces ⋮ Quantum harmonic analysis on lattices and Gabor multipliers ⋮ Weyl–Wigner formulation of noncommutative quantum mechanics ⋮ Characters and contact transformations ⋮ Localization of multidimensional Wigner distributions ⋮ Quantum U-statistics ⋮ Modulation spaces and pseudodifferential operators ⋮ Time-frequency localization operators and a Berezin transform ⋮ Cyclic vectors for Hilbert algebras ⋮ Wigner functions on non-standard symplectic vector spaces ⋮ Foundations of phase-space quantum mechanics ⋮ Polar decomposition and isometric integral transforms∗
Cites Work
- The \(C^ *\)-algebras of a free Boson field
- Continuous-Representation Theory. IV. Structure of a Class of Function Spaces Arising from Quantum Mechanics
- Phase-Space Formulation of the Dynamics of Canonical Variables
- Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group.
This page was built for publication: Mathematical Aspects of the Weyl Correspondence