The Stratonovich–Weyl correspondence for one-dimensional kinematical groups

DOI10.1063/1.529315zbMath0746.22016OpenAlexW2000526239MaRDI QIDQ3981680

Miguel Angel Martín, Luis-Miguel Nieto, Mariano A. del Olmo, Manuel Gadella

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529315

zbMATH Keywords

Hilbert spacephase spacecoadjoint orbitsself-adjoint operatorsgroup of transformationsStratonovich-Weyl correspondenceMoyal quantizationtwo-dimensional Euclidean group

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Geometric quantization (53D50) Applications of operator theory in probability theory and statistics (47N30)

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Cites Work

• Galilei-Newton law by symplectic realizations
• The Moyal representation for spin
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• Locally operating realizations of transformation Lie groups
• Projective covering group versus representation groups
• On the Quantum Correction For Thermodynamic Equilibrium
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• Mackey-Moore cohomology and topological extensions of Polish groups
• Possible Kinematics