On the regular Hilbert space representation of a Moyal quantization

DOI10.1063/1.530537zbMath0848.47042OpenAlexW2025559254MaRDI QIDQ4314195

Günter Braunss

Publication date: 16 October 1996

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

Full work available at URL: https://doi.org/10.1063/1.530537

zbMATH Keywords

quantum entropyessentially selfadjoint operatorsboundedness of Moyal operatorsphase space representation of a Moyal quantizationreal polynomials in the phase space variables

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) General quantum mechanics and problems of quantization (81S99)

Related Items (2)

Quantum dynamics in phase space: Moyal trajectories 3 ⋮ Quantum dynamics in phase space: Moyal trajectories 2

Cites Work

• General concept of quantization
• Models of Gross-Neveu type are quantization of a classical mechanics with nonlinear phase space
• Remarks on the relation between quantum and classical entropy as proposed by A. Wehrl
• The Moyal representation of quantum mechanics and special function theory
• An explicit *-product on the cotangent bundle of a Lie group
• Quantization and the uniqueness of invariant structures
• Deformation theory applied to quantization and statistical mechanics
• Wehrl-Lieb's inequality for entropy and the uncertainty relation
• Conformal symplectic geometry, deformations, rigidity and geometrical (KMS) conditions
• Causal phase-space approach to fermion theories understood through Clifford algebras
• Cohomology and deformations of Lie superalgebras
• On the relation between classical and quantum-mechanical entropy
• The algebra of Weyl symmetrised polynomials and its quantum extension
• Coherent states and geometric quantization
• Deformation theory and quantization. I: Deformations of symplectic structures
• Proof of an entropy conjecture of Wehrl
• Algebraic quantization
• Deformations and renormalisations of \(W_{\infty}\)
• Quantum harmonic analysis on phase space
• Bilinear phase-plane distribution functions and positivity
• The problem of moments in the phase-space formulation of quantum mechanics
• Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra
• The formulation of quantum mechanics in terms of phase space functions-the third equation
• On the Quantum Correction For Thermodynamic Equilibrium

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