Wigner–Weyl isomorphism for quantum mechanics on Lie groups

DOI10.1063/1.1825078zbMath1076.81026arXivquant-ph/0407257OpenAlexW3103467612WikidataQ115333648 ScholiaQ115333648MaRDI QIDQ3024171

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Publication date: 30 June 2005

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

Full work available at URL: https://arxiv.org/abs/quant-ph/0407257

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

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Correspondence rules for Wigner functions over $SU(3)/U(2)$ ⋮ Coherent states in magnetized anisotropic 2D Dirac materials ⋮ GeneralizedSU(2) covariant Wigner functions and some of their applications ⋮ Orbital angular momentum in phase space ⋮ Schwinger representation for the symmetric group:Two explicit constructions for the carrier space ⋮ Discrete phase-space mappings, tomographic condition and permutation invariance ⋮ Wigner function for the orientation state ⋮ Semiclassical dynamics of a rigid rotor: SO(3) covariant approach ⋮ Minimum uncertainty states in angular momentum and angle variables for charged particles in structured electromagnetic fields ⋮ THE SCHWINGER REPRESENTATION OF A GROUP: CONCEPT AND APPLICATIONS ⋮ On teleparallel quantum gravity in Schwarzschild space-time

Cites Work

• *-products on \(D^ 1(C)\), \(S^ 2\) and related spectral analysis
• The Moyal representation for spin
• Some ideas about quantization
• Wigner distributions for non-Abelian finite groups of odd order
• Quantum mechanics another way
• Group theory and quasiprobability integrals of Wigner functions
• Wigner distributions and quantum mechanics on Lie groups: The case of the regular representation
• On the principles of elementary quantum mechanics

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